diff --git a/src/installer/utils.py b/src/installer/utils.py
index cb412d72..18955adb 100644
--- a/src/installer/utils.py
+++ b/src/installer/utils.py
@@ -109,7 +109,9 @@ def parse_wheel_filename(filename: str) -> WheelFilename:
     wheel_info = _WHEEL_FILENAME_REGEX.match(filename)
     if not wheel_info:
         raise ValueError(f"Not a valid wheel filename: {filename}")
-    return WheelFilename(*wheel_info.groups())
+    parsed = wheel_info.groups()
+    normalized_name = normalize_distribution_name(parsed[0])
+    return WheelFilename(normalized_name, *parsed[1:])
 
 
 def copyfileobj_with_hashing(
diff --git a/tests/test_utils.py b/tests/test_utils.py
index bf59962e..883145ea 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -93,6 +93,11 @@ class TestParseWheelFilename:
                 "tensorflow-2.3.0-cp38-cp38-win_amd64.whl",
                 WheelFilename("tensorflow", "2.3.0", None, "cp38-cp38-win_amd64"),
             ),
+            # Non-canonicalized real wheel names
+            (
+                "Quart-0.18.0-py3-none-any.whl",
+                WheelFilename("quart", "0.18.0", None, "py3-none-any"),
+            ),
         ],
     )
     def test_valid_cases(self, string, expected):