diff --git a/docs/news.rst b/docs/news.rst
index 4fc4f4ca..30866221 100644
--- a/docs/news.rst
+++ b/docs/news.rst
@@ -4,6 +4,7 @@ Release Notes
 **UNRELEASED**
 
 - Fixed ``wheel pack`` duplicating the ``WHEEL`` contents when the build number has changed (#415)
+- Fixed normalization of the ``.dist-info`` directory in wheels to conform to the PyPA spec (#441)
 
 **0.37.0 (2021-08-09)**
 
diff --git a/src/wheel/cli/unpack.py b/src/wheel/cli/unpack.py
index 2e9857a3..5084e5e4 100644
--- a/src/wheel/cli/unpack.py
+++ b/src/wheel/cli/unpack.py
@@ -16,8 +16,9 @@ def unpack(path, dest='.'):
     :param dest: Destination directory (default to current directory).
     """
     with WheelFile(path) as wf:
-        namever = wf.parsed_filename.group('namever')
-        destination = os.path.join(dest, namever)
+        name, version = os.path.basename(path).split('-', 2)[:2]
+        dirname = name + '-' + version
+        destination = os.path.join(dest, dirname)
         print("Unpacking to: {}...".format(destination), end='')
         sys.stdout.flush()
         wf.extractall(destination)
diff --git a/src/wheel/vendored/packaging/_structures.py b/src/wheel/vendored/packaging/_structures.py
new file mode 100644
index 00000000..800d5c55
--- /dev/null
+++ b/src/wheel/vendored/packaging/_structures.py
@@ -0,0 +1,86 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+from __future__ import absolute_import, division, print_function
+
+
+class InfinityType(object):
+    def __repr__(self):
+        # type: () -> str
+        return "Infinity"
+
+    def __hash__(self):
+        # type: () -> int
+        return hash(repr(self))
+
+    def __lt__(self, other):
+        # type: (object) -> bool
+        return False
+
+    def __le__(self, other):
+        # type: (object) -> bool
+        return False
+
+    def __eq__(self, other):
+        # type: (object) -> bool
+        return isinstance(other, self.__class__)
+
+    def __ne__(self, other):
+        # type: (object) -> bool
+        return not isinstance(other, self.__class__)
+
+    def __gt__(self, other):
+        # type: (object) -> bool
+        return True
+
+    def __ge__(self, other):
+        # type: (object) -> bool
+        return True
+
+    def __neg__(self):
+        # type: (object) -> NegativeInfinityType
+        return NegativeInfinity
+
+
+Infinity = InfinityType()
+
+
+class NegativeInfinityType(object):
+    def __repr__(self):
+        # type: () -> str
+        return "-Infinity"
+
+    def __hash__(self):
+        # type: () -> int
+        return hash(repr(self))
+
+    def __lt__(self, other):
+        # type: (object) -> bool
+        return True
+
+    def __le__(self, other):
+        # type: (object) -> bool
+        return True
+
+    def __eq__(self, other):
+        # type: (object) -> bool
+        return isinstance(other, self.__class__)
+
+    def __ne__(self, other):
+        # type: (object) -> bool
+        return not isinstance(other, self.__class__)
+
+    def __gt__(self, other):
+        # type: (object) -> bool
+        return False
+
+    def __ge__(self, other):
+        # type: (object) -> bool
+        return False
+
+    def __neg__(self):
+        # type: (object) -> InfinityType
+        return Infinity
+
+
+NegativeInfinity = NegativeInfinityType()
diff --git a/src/wheel/vendored/packaging/utils.py b/src/wheel/vendored/packaging/utils.py
new file mode 100644
index 00000000..6e8c2a3e
--- /dev/null
+++ b/src/wheel/vendored/packaging/utils.py
@@ -0,0 +1,138 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+from __future__ import absolute_import, division, print_function
+
+import re
+
+from ._typing import TYPE_CHECKING, cast
+from .tags import Tag, parse_tag
+from .version import InvalidVersion, Version
+
+if TYPE_CHECKING:  # pragma: no cover
+    from typing import FrozenSet, NewType, Tuple, Union
+
+    BuildTag = Union[Tuple[()], Tuple[int, str]]
+    NormalizedName = NewType("NormalizedName", str)
+else:
+    BuildTag = tuple
+    NormalizedName = str
+
+
+class InvalidWheelFilename(ValueError):
+    """
+    An invalid wheel filename was found, users should refer to PEP 427.
+    """
+
+
+class InvalidSdistFilename(ValueError):
+    """
+    An invalid sdist filename was found, users should refer to the packaging user guide.
+    """
+
+
+_canonicalize_regex = re.compile(r"[-_.]+")
+# PEP 427: The build number must start with a digit.
+_build_tag_regex = re.compile(r"(\d+)(.*)")
+
+
+def canonicalize_name(name):
+    # type: (str) -> NormalizedName
+    # This is taken from PEP 503.
+    value = _canonicalize_regex.sub("-", name).lower()
+    return cast(NormalizedName, value)
+
+
+def canonicalize_version(version):
+    # type: (Union[Version, str]) -> Union[Version, str]
+    """
+    This is very similar to Version.__str__, but has one subtle difference
+    with the way it handles the release segment.
+    """
+    if not isinstance(version, Version):
+        try:
+            version = Version(version)
+        except InvalidVersion:
+            # Legacy versions cannot be normalized
+            return version
+
+    parts = []
+
+    # Epoch
+    if version.epoch != 0:
+        parts.append("{0}!".format(version.epoch))
+
+    # Release segment
+    # NB: This strips trailing '.0's to normalize
+    parts.append(re.sub(r"(\.0)+$", "", ".".join(str(x) for x in version.release)))
+
+    # Pre-release
+    if version.pre is not None:
+        parts.append("".join(str(x) for x in version.pre))
+
+    # Post-release
+    if version.post is not None:
+        parts.append(".post{0}".format(version.post))
+
+    # Development release
+    if version.dev is not None:
+        parts.append(".dev{0}".format(version.dev))
+
+    # Local version segment
+    if version.local is not None:
+        parts.append("+{0}".format(version.local))
+
+    return "".join(parts)
+
+
+def parse_wheel_filename(filename):
+    # type: (str) -> Tuple[NormalizedName, Version, BuildTag, FrozenSet[Tag]]
+    if not filename.endswith(".whl"):
+        raise InvalidWheelFilename(
+            "Invalid wheel filename (extension must be '.whl'): {0}".format(filename)
+        )
+
+    filename = filename[:-4]
+    dashes = filename.count("-")
+    if dashes not in (4, 5):
+        raise InvalidWheelFilename(
+            "Invalid wheel filename (wrong number of parts): {0}".format(filename)
+        )
+
+    parts = filename.split("-", dashes - 2)
+    name_part = parts[0]
+    # See PEP 427 for the rules on escaping the project name
+    if "__" in name_part or re.match(r"^[\w\d._]*$", name_part, re.UNICODE) is None:
+        raise InvalidWheelFilename("Invalid project name: {0}".format(filename))
+    name = canonicalize_name(name_part)
+    version = Version(parts[1])
+    if dashes == 5:
+        build_part = parts[2]
+        build_match = _build_tag_regex.match(build_part)
+        if build_match is None:
+            raise InvalidWheelFilename(
+                "Invalid build number: {0} in '{1}'".format(build_part, filename)
+            )
+        build = cast(BuildTag, (int(build_match.group(1)), build_match.group(2)))
+    else:
+        build = ()
+    tags = parse_tag(parts[-1])
+    return (name, version, build, tags)
+
+
+def parse_sdist_filename(filename):
+    # type: (str) -> Tuple[NormalizedName, Version]
+    if not filename.endswith(".tar.gz"):
+        raise InvalidSdistFilename(
+            "Invalid sdist filename (extension must be '.tar.gz'): {0}".format(filename)
+        )
+
+    # We are requiring a PEP 440 version, which cannot contain dashes,
+    # so we split on the last dash.
+    name_part, sep, version_part = filename[:-7].rpartition("-")
+    if not sep:
+        raise InvalidSdistFilename("Invalid sdist filename: {0}".format(filename))
+
+    name = canonicalize_name(name_part)
+    version = Version(version_part)
+    return (name, version)
diff --git a/src/wheel/vendored/packaging/version.py b/src/wheel/vendored/packaging/version.py
new file mode 100644
index 00000000..517d91f2
--- /dev/null
+++ b/src/wheel/vendored/packaging/version.py
@@ -0,0 +1,556 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+from __future__ import absolute_import, division, print_function
+
+import collections
+import itertools
+import re
+import warnings
+
+from ._structures import Infinity, NegativeInfinity
+from ._typing import TYPE_CHECKING
+
+if TYPE_CHECKING:  # pragma: no cover
+    from typing import Callable, Iterator, List, Optional, SupportsInt, Tuple, Union
+
+    from ._structures import InfinityType, NegativeInfinityType
+
+    InfiniteTypes = Union[InfinityType, NegativeInfinityType]
+    PrePostDevType = Union[InfiniteTypes, Tuple[str, int]]
+    SubLocalType = Union[InfiniteTypes, int, str]
+    LocalType = Union[
+        NegativeInfinityType,
+        Tuple[
+            Union[
+                SubLocalType,
+                Tuple[SubLocalType, str],
+                Tuple[NegativeInfinityType, SubLocalType],
+            ],
+            ...,
+        ],
+    ]
+    CmpKey = Tuple[
+        int, Tuple[int, ...], PrePostDevType, PrePostDevType, PrePostDevType, LocalType
+    ]
+    LegacyCmpKey = Tuple[int, Tuple[str, ...]]
+    VersionComparisonMethod = Callable[
+        [Union[CmpKey, LegacyCmpKey], Union[CmpKey, LegacyCmpKey]], bool
+    ]
+
+__all__ = ["parse", "Version", "LegacyVersion", "InvalidVersion", "VERSION_PATTERN"]
+
+
+_Version = collections.namedtuple(
+    "_Version", ["epoch", "release", "dev", "pre", "post", "local"]
+)
+
+
+def parse(version):
+    # type: (str) -> Union[LegacyVersion, Version]
+    """
+    Parse the given version string and return either a :class:`Version` object
+    or a :class:`LegacyVersion` object depending on if the given version is
+    a valid PEP 440 version or a legacy version.
+    """
+    try:
+        return Version(version)
+    except InvalidVersion:
+        return LegacyVersion(version)
+
+
+class InvalidVersion(ValueError):
+    """
+    An invalid version was found, users should refer to PEP 440.
+    """
+
+
+class _BaseVersion(object):
+    _key = None  # type: Union[CmpKey, LegacyCmpKey]
+
+    def __hash__(self):
+        # type: () -> int
+        return hash(self._key)
+
+    # Please keep the duplicated `isinstance` check
+    # in the six comparisons hereunder
+    # unless you find a way to avoid adding overhead function calls.
+    def __lt__(self, other):
+        # type: (_BaseVersion) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key < other._key
+
+    def __le__(self, other):
+        # type: (_BaseVersion) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key <= other._key
+
+    def __eq__(self, other):
+        # type: (object) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key == other._key
+
+    def __ge__(self, other):
+        # type: (_BaseVersion) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key >= other._key
+
+    def __gt__(self, other):
+        # type: (_BaseVersion) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key > other._key
+
+    def __ne__(self, other):
+        # type: (object) -> bool
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key != other._key
+
+
+class LegacyVersion(_BaseVersion):
+    def __init__(self, version):
+        # type: (str) -> None
+        self._version = str(version)
+        self._key = _legacy_cmpkey(self._version)
+
+        warnings.warn(
+            "Creating a LegacyVersion has been deprecated and will be "
+            "removed in the next major release",
+            DeprecationWarning,
+        )
+
+    def __str__(self):
+        # type: () -> str
+        return self._version
+
+    def __repr__(self):
+        # type: () -> str
+        return "<LegacyVersion({0})>".format(repr(str(self)))
+
+    @property
+    def public(self):
+        # type: () -> str
+        return self._version
+
+    @property
+    def base_version(self):
+        # type: () -> str
+        return self._version
+
+    @property
+    def epoch(self):
+        # type: () -> int
+        return -1
+
+    @property
+    def release(self):
+        # type: () -> None
+        return None
+
+    @property
+    def pre(self):
+        # type: () -> None
+        return None
+
+    @property
+    def post(self):
+        # type: () -> None
+        return None
+
+    @property
+    def dev(self):
+        # type: () -> None
+        return None
+
+    @property
+    def local(self):
+        # type: () -> None
+        return None
+
+    @property
+    def is_prerelease(self):
+        # type: () -> bool
+        return False
+
+    @property
+    def is_postrelease(self):
+        # type: () -> bool
+        return False
+
+    @property
+    def is_devrelease(self):
+        # type: () -> bool
+        return False
+
+
+_legacy_version_component_re = re.compile(r"(\d+ | [a-z]+ | \.| -)", re.VERBOSE)
+
+_legacy_version_replacement_map = {
+    "pre": "c",
+    "preview": "c",
+    "-": "final-",
+    "rc": "c",
+    "dev": "@",
+}
+
+
+def _parse_version_parts(s):
+    # type: (str) -> Iterator[str]
+    for part in _legacy_version_component_re.split(s):
+        part = _legacy_version_replacement_map.get(part, part)
+
+        if not part or part == ".":
+            continue
+
+        if part[:1] in "0123456789":
+            # pad for numeric comparison
+            yield part.zfill(8)
+        else:
+            yield "*" + part
+
+    # ensure that alpha/beta/candidate are before final
+    yield "*final"
+
+
+def _legacy_cmpkey(version):
+    # type: (str) -> LegacyCmpKey
+
+    # We hardcode an epoch of -1 here. A PEP 440 version can only have a epoch
+    # greater than or equal to 0. This will effectively put the LegacyVersion,
+    # which uses the defacto standard originally implemented by setuptools,
+    # as before all PEP 440 versions.
+    epoch = -1
+
+    # This scheme is taken from pkg_resources.parse_version setuptools prior to
+    # it's adoption of the packaging library.
+    parts = []  # type: List[str]
+    for part in _parse_version_parts(version.lower()):
+        if part.startswith("*"):
+            # remove "-" before a prerelease tag
+            if part < "*final":
+                while parts and parts[-1] == "*final-":
+                    parts.pop()
+
+            # remove trailing zeros from each series of numeric parts
+            while parts and parts[-1] == "00000000":
+                parts.pop()
+
+        parts.append(part)
+
+    return epoch, tuple(parts)
+
+
+# Deliberately not anchored to the start and end of the string, to make it
+# easier for 3rd party code to reuse
+VERSION_PATTERN = r"""
+    v?
+    (?:
+        (?:(?P<epoch>[0-9]+)!)?                           # epoch
+        (?P<release>[0-9]+(?:\.[0-9]+)*)                  # release segment
+        (?P<pre>                                          # pre-release
+            [-_\.]?
+            (?P<pre_l>(a|b|c|rc|alpha|beta|pre|preview))
+            [-_\.]?
+            (?P<pre_n>[0-9]+)?
+        )?
+        (?P<post>                                         # post release
+            (?:-(?P<post_n1>[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?P<post_l>post|rev|r)
+                [-_\.]?
+                (?P<post_n2>[0-9]+)?
+            )
+        )?
+        (?P<dev>                                          # dev release
+            [-_\.]?
+            (?P<dev_l>dev)
+            [-_\.]?
+            (?P<dev_n>[0-9]+)?
+        )?
+    )
+    (?:\+(?P<local>[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+
+class Version(_BaseVersion):
+
+    _regex = re.compile(r"^\s*" + VERSION_PATTERN + r"\s*$", re.VERBOSE | re.IGNORECASE)
+
+    def __init__(self, version):
+        # type: (str) -> None
+
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion("Invalid version: '{0}'".format(version))
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(match.group("pre_l"), match.group("pre_n")),
+            post=_parse_letter_version(
+                match.group("post_l"), match.group("post_n1") or match.group("post_n2")
+            ),
+            dev=_parse_letter_version(match.group("dev_l"), match.group("dev_n")),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self):
+        # type: () -> str
+        return "<Version({0})>".format(repr(str(self)))
+
+    def __str__(self):
+        # type: () -> str
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append("{0}!".format(self.epoch))
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        # Pre-release
+        if self.pre is not None:
+            parts.append("".join(str(x) for x in self.pre))
+
+        # Post-release
+        if self.post is not None:
+            parts.append(".post{0}".format(self.post))
+
+        # Development release
+        if self.dev is not None:
+            parts.append(".dev{0}".format(self.dev))
+
+        # Local version segment
+        if self.local is not None:
+            parts.append("+{0}".format(self.local))
+
+        return "".join(parts)
+
+    @property
+    def epoch(self):
+        # type: () -> int
+        _epoch = self._version.epoch  # type: int
+        return _epoch
+
+    @property
+    def release(self):
+        # type: () -> Tuple[int, ...]
+        _release = self._version.release  # type: Tuple[int, ...]
+        return _release
+
+    @property
+    def pre(self):
+        # type: () -> Optional[Tuple[str, int]]
+        _pre = self._version.pre  # type: Optional[Tuple[str, int]]
+        return _pre
+
+    @property
+    def post(self):
+        # type: () -> Optional[Tuple[str, int]]
+        return self._version.post[1] if self._version.post else None
+
+    @property
+    def dev(self):
+        # type: () -> Optional[Tuple[str, int]]
+        return self._version.dev[1] if self._version.dev else None
+
+    @property
+    def local(self):
+        # type: () -> Optional[str]
+        if self._version.local:
+            return ".".join(str(x) for x in self._version.local)
+        else:
+            return None
+
+    @property
+    def public(self):
+        # type: () -> str
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self):
+        # type: () -> str
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append("{0}!".format(self.epoch))
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        return "".join(parts)
+
+    @property
+    def is_prerelease(self):
+        # type: () -> bool
+        return self.dev is not None or self.pre is not None
+
+    @property
+    def is_postrelease(self):
+        # type: () -> bool
+        return self.post is not None
+
+    @property
+    def is_devrelease(self):
+        # type: () -> bool
+        return self.dev is not None
+
+    @property
+    def major(self):
+        # type: () -> int
+        return self.release[0] if len(self.release) >= 1 else 0
+
+    @property
+    def minor(self):
+        # type: () -> int
+        return self.release[1] if len(self.release) >= 2 else 0
+
+    @property
+    def micro(self):
+        # type: () -> int
+        return self.release[2] if len(self.release) >= 3 else 0
+
+
+def _parse_letter_version(
+    letter,  # type: str
+    number,  # type: Union[str, bytes, SupportsInt]
+):
+    # type: (...) -> Optional[Tuple[str, int]]
+
+    if letter:
+        # We consider there to be an implicit 0 in a pre-release if there is
+        # not a numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume if we are given a number, but we are not given a letter
+        # then this is using the implicit post release syntax (e.g. 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+    return None
+
+
+_local_version_separators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local):
+    # type: (str) -> Optional[LocalType]
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_separators.split(local)
+        )
+    return None
+
+
+def _cmpkey(
+    epoch,  # type: int
+    release,  # type: Tuple[int, ...]
+    pre,  # type: Optional[Tuple[str, int]]
+    post,  # type: Optional[Tuple[str, int]]
+    dev,  # type: Optional[Tuple[str, int]]
+    local,  # type: Optional[Tuple[SubLocalType]]
+):
+    # type: (...) -> CmpKey
+
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non zero, then take the rest
+    # re-reverse it back into the correct order and make it a tuple and use
+    # that for our sorting key.
+    _release = tuple(
+        reversed(list(itertools.dropwhile(lambda x: x == 0, reversed(release))))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre segment, but we _only_ want to do this
+    # if there is not a pre or a post segment. If we have one of those then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        _pre = NegativeInfinity  # type: PrePostDevType
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        _pre = Infinity
+    else:
+        _pre = pre
+
+    # Versions without a post segment should sort before those with one.
+    if post is None:
+        _post = NegativeInfinity  # type: PrePostDevType
+
+    else:
+        _post = post
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        _dev = Infinity  # type: PrePostDevType
+
+    else:
+        _dev = dev
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        _local = NegativeInfinity  # type: LocalType
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alpha numeric segments sort before numeric segments
+        # - Alpha numeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        _local = tuple(
+            (i, "") if isinstance(i, int) else (NegativeInfinity, i) for i in local
+        )
+
+    return epoch, _release, _pre, _post, _dev, _local
diff --git a/src/wheel/wheelfile.py b/src/wheel/wheelfile.py
index 3ee97ddd..71def8a0 100644
--- a/src/wheel/wheelfile.py
+++ b/src/wheel/wheelfile.py
@@ -3,22 +3,15 @@
 import csv
 import hashlib
 import os.path
-import re
 import stat
 import time
 from collections import OrderedDict
 from distutils import log as logger
 from zipfile import ZIP_DEFLATED, ZipInfo, ZipFile
 
-from wheel.cli import WheelError
-from wheel.util import urlsafe_b64decode, as_unicode, native, urlsafe_b64encode, as_bytes, StringIO
-
-# Non-greedy matching of an optional build number may be too clever (more
-# invalid wheel filenames will match). Separate regex for .dist-info?
-WHEEL_INFO_RE = re.compile(
-    r"""^(?P<namever>(?P<name>.+?)-(?P<ver>.+?))(-(?P<build>\d[^-]*))?
-     -(?P<pyver>.+?)-(?P<abi>.+?)-(?P<plat>.+?)\.whl$""",
-    re.VERBOSE)
+from .cli import WheelError
+from .util import urlsafe_b64decode, as_unicode, native, urlsafe_b64encode, as_bytes, StringIO
+from .vendored.packaging.utils import InvalidWheelFilename, parse_wheel_filename
 
 
 def get_zipinfo_datetime(timestamp=None):
@@ -37,13 +30,15 @@ class WheelFile(ZipFile):
 
     def __init__(self, file, mode='r', compression=ZIP_DEFLATED):
         basename = os.path.basename(file)
-        self.parsed_filename = WHEEL_INFO_RE.match(basename)
-        if not basename.endswith('.whl') or self.parsed_filename is None:
+        try:
+            name, version, build, tags = parse_wheel_filename(basename)
+        except InvalidWheelFilename:
             raise WheelError("Bad wheel filename {!r}".format(basename))
 
+        name = name.replace('-', '_')
         ZipFile.__init__(self, file, mode, compression=compression, allowZip64=True)
 
-        self.dist_info_path = '{}.dist-info'.format(self.parsed_filename.group('namever'))
+        self.dist_info_path = '{name}-{version}.dist-info'.format(name=name, version=version)
         self.record_path = self.dist_info_path + '/RECORD'
         self._file_hashes = OrderedDict()
         self._file_sizes = {}
@@ -57,7 +52,20 @@ def __init__(self, file, mode='r', compression=ZIP_DEFLATED):
             try:
                 record = self.open(self.record_path)
             except KeyError:
-                raise WheelError('Missing {} file'.format(self.record_path))
+                # Try again with the old, denormalized .dist-info path
+                name, version = basename.split('-', 2)[:2]
+                del self._file_hashes[self.record_path]
+                del self._file_hashes[self.record_path + '.jws']
+                del self._file_hashes[self.record_path + '.p7s']
+                self.dist_info_path = '{}-{}.dist-info'.format(name, version)
+                self.record_path = self.dist_info_path + '/RECORD'
+                self._file_hashes[self.record_path] = None, None
+                self._file_hashes[self.record_path + '.jws'] = None, None
+                self._file_hashes[self.record_path + '.p7s'] = None, None
+                try:
+                    record = self.open(self.record_path)
+                except KeyError:
+                    raise WheelError('Missing RECORD file')
 
             with record:
                 for line in record:
diff --git a/tests/cli/test_convert.py b/tests/cli/test_convert.py
index 7d711aa8..ece55fcc 100644
--- a/tests/cli/test_convert.py
+++ b/tests/cli/test_convert.py
@@ -1,8 +1,7 @@
 import os.path
-import re
 
 from wheel.cli.convert import convert, egg_info_re
-from wheel.wheelfile import WHEEL_INFO_RE
+from wheel.vendored.packaging.utils import parse_wheel_filename
 
 
 def test_egg_re():
@@ -19,6 +18,5 @@ def test_convert_egg(egg_paths, tmpdir):
     convert(egg_paths, str(tmpdir), verbose=False)
     wheel_names = [path.basename for path in tmpdir.listdir()]
     assert len(wheel_names) == len(egg_paths)
-    assert all(WHEEL_INFO_RE.match(filename) for filename in wheel_names)
-    assert all(re.match(r'^[\w\d.]+-\d\.\d-\w+\d+-[\w\d]+-[\w\d]+\.whl$', fname)
-               for fname in wheel_names)
+    for fname in wheel_names:
+        parse_wheel_filename(fname)
diff --git a/tests/test_bdist_wheel.py b/tests/test_bdist_wheel.py
index 651c0345..9c0e2c4d 100644
--- a/tests/test_bdist_wheel.py
+++ b/tests/test_bdist_wheel.py
@@ -56,7 +56,7 @@ def test_no_scripts(wheel_paths):
 def test_unicode_record(wheel_paths):
     path = next(path for path in wheel_paths if 'unicode.dist' in path)
     with ZipFile(path) as zf:
-        record = zf.read('unicode.dist-0.1.dist-info/RECORD')
+        record = zf.read('unicode_dist-0.1.dist-info/RECORD')
 
     assert u'åäö_日本語.py'.encode('utf-8') in record
 
diff --git a/tests/test_wheelfile.py b/tests/test_wheelfile.py
index db11bcd2..cf9f9359 100644
--- a/tests/test_wheelfile.py
+++ b/tests/test_wheelfile.py
@@ -20,7 +20,7 @@ def test_wheelfile_re(tmpdir):
     # Regression test for #208
     path = tmpdir.join('foo-2-py3-none-any.whl')
     with WheelFile(str(path), 'w') as wf:
-        assert wf.parsed_filename.group('namever') == 'foo-2'
+        assert wf.dist_info_path == 'foo-2.dist-info'
 
 
 @pytest.mark.parametrize('filename', [
@@ -40,7 +40,7 @@ def test_missing_record(wheel_path):
         zf.writestr(native('hello/héllö.py'), as_bytes('print("Héllö, w0rld!")\n'))
 
     exc = pytest.raises(WheelError, WheelFile, wheel_path)
-    exc.match("^Missing test-1.0.dist-info/RECORD file$")
+    exc.match("^Missing RECORD file$")
 
 
 def test_unsupported_hash_algorithm(wheel_path):