diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index 09d56eed6..4f82e4a10 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -29,6 +29,7 @@ from django.utils.encoding import is_protected_type, smart_str
 from django.utils.formats import localize_input, sanitize_separators
 from django.utils.ipv6 import clean_ipv6_address
 from django.utils.translation import gettext_lazy as _
+from pytz.exceptions import InvalidTimeError
 
 from rest_framework import ISO_8601
 from rest_framework.exceptions import ErrorDetail, ValidationError
@@ -1161,12 +1162,15 @@ class DateTimeField(Field):
                     return value.astimezone(field_timezone)
                 except OverflowError:
                     self.fail('overflow')
-            dt = timezone.make_aware(value, field_timezone)
-            # When the resulting datetime is a ZoneInfo instance, it won't necessarily
-            # throw given an invalid datetime, so we need to specifically check.
-            if not valid_datetime(dt):
+            try:
+                dt = timezone.make_aware(value, field_timezone)
+                # When the resulting datetime is a ZoneInfo instance, it won't necessarily
+                # throw given an invalid datetime, so we need to specifically check.
+                if not valid_datetime(dt):
+                    self.fail('make_aware', timezone=field_timezone)
+                return dt
+            except InvalidTimeError:
                 self.fail('make_aware', timezone=field_timezone)
-            return dt
         elif (field_timezone is None) and timezone.is_aware(value):
             return timezone.make_naive(value, datetime.timezone.utc)
         return value
diff --git a/setup.py b/setup.py
index 6afd5e05e..533ffa97f 100755
--- a/setup.py
+++ b/setup.py
@@ -83,7 +83,7 @@ setup(
     author_email='tom@tomchristie.com',  # SEE NOTE BELOW (*)
     packages=find_packages(exclude=['tests*']),
     include_package_data=True,
-    install_requires=["django>=3.0", 'backports.zoneinfo;python_version<"3.9"'],
+    install_requires=["django>=3.0", "pytz", 'backports.zoneinfo;python_version<"3.9"'],
     python_requires=">=3.6",
     zip_safe=False,
     classifiers=[
diff --git a/tests/test_fields.py b/tests/test_fields.py
index 189819c68..bcf388441 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -9,6 +9,7 @@ from enum import auto
 from unittest.mock import patch
 
 import pytest
+import pytz
 from django.core.exceptions import ValidationError as DjangoValidationError
 from django.db.models import IntegerChoices, TextChoices
 from django.http import QueryDict
@@ -1589,6 +1590,31 @@ class TestCustomTimezoneForDateTimeField(TestCase):
         assert rendered_date == rendered_date_in_timezone
 
 
+@pytest.mark.skipif(pytz is None, reason="As Django 4.0 has deprecated pytz, this test should eventually be able to get removed.")
+class TestPytzNaiveDayLightSavingTimeTimeZoneDateTimeField(FieldValues):
+    """
+    Invalid values for `DateTimeField` with datetime in DST shift (non-existing or ambiguous) and timezone with DST.
+    Timezone America/New_York has DST shift from 2017-03-12T02:00:00 to 2017-03-12T03:00:00 and
+     from 2017-11-05T02:00:00 to 2017-11-05T01:00:00 in 2017.
+    """
+    valid_inputs = {}
+    invalid_inputs = {
+        '2017-03-12T02:30:00': ['Invalid datetime for the timezone "America/New_York".'],
+        '2017-11-05T01:30:00': ['Invalid datetime for the timezone "America/New_York".']
+    }
+    outputs = {}
+
+    class MockTimezone(pytz.BaseTzInfo):
+        @staticmethod
+        def localize(value, is_dst):
+            raise pytz.InvalidTimeError()
+
+        def __str__(self):
+            return 'America/New_York'
+
+    field = serializers.DateTimeField(default_timezone=MockTimezone())
+
+
 @patch('rest_framework.utils.timezone.datetime_ambiguous', return_value=True)
 class TestNaiveDayLightSavingTimeTimeZoneDateTimeField(FieldValues):
     """