diff --git a/distutils/command/install.py b/distutils/command/install.py
index 511938f47f..9fe659131f 100644
--- a/distutils/command/install.py
+++ b/distutils/command/install.py
@@ -68,8 +68,8 @@
     INSTALL_SCHEMES['nt_user'] = {
         'purelib': '{usersite}',
         'platlib': '{usersite}',
-        'headers': '{userbase}/{implementation}{py_version_nodot}/Include/{dist_name}',
-        'scripts': '{userbase}/{implementation}{py_version_nodot}/Scripts',
+        'headers': '{userbase}/{implementation}{py_version_nodot_plat}/Include/{dist_name}',
+        'scripts': '{userbase}/{implementation}{py_version_nodot_plat}/Scripts',
         'data'   : '{userbase}',
         }
 
@@ -412,12 +412,18 @@ def finalize_options(self):
                             'implementation': _get_implementation(),
                            }
 
+        # vars for compatibility on older Pythons
+        compat_vars = dict(
+            # Python 3.9 and earlier
+            py_version_nodot_plat=getattr(sys, 'winver', '').replace('.', ''),
+        )
+
         if HAS_USER_SITE:
             local_vars['userbase'] = self.install_userbase
             local_vars['usersite'] = self.install_usersite
 
         self.config_vars = _collections.DictStack(
-            [sysconfig.get_config_vars(), local_vars])
+            [compat_vars, sysconfig.get_config_vars(), local_vars])
 
         self.expand_basedirs()
 
diff --git a/distutils/tests/test_install.py b/distutils/tests/test_install.py
index 75770b05e6..5dbc06b090 100644
--- a/distutils/tests/test_install.py
+++ b/distutils/tests/test_install.py
@@ -81,7 +81,9 @@ def test_user_site(self):
         install_module.USER_SITE = self.user_site
 
         def _expanduser(path):
-            return self.tmpdir
+            if path.startswith('~'):
+                return os.path.normpath(self.tmpdir + path[1:])
+            return path
         self.old_expand = os.path.expanduser
         os.path.expanduser = _expanduser
 
@@ -122,6 +124,17 @@ def cleanup():
         self.assertIn('userbase', cmd.config_vars)
         self.assertIn('usersite', cmd.config_vars)
 
+        actual_headers = os.path.relpath(cmd.install_headers, self.user_base)
+        if os.name == 'nt':
+            site_path = os.path.relpath(
+                os.path.dirname(self.old_user_site), self.old_user_base)
+            include = os.path.join(site_path, 'Include')
+        else:
+            include = sysconfig.get_python_inc(0, '')
+        expect_headers = os.path.join(include, 'xx')
+
+        self.assertEqual(os.path.normcase(actual_headers), os.path.normcase(expect_headers))
+
     def test_handle_extra_path(self):
         dist = Distribution({'name': 'xx', 'extra_path': 'path,dirs'})
         cmd = install(dist)