diff --git a/rest_framework/compat.py b/rest_framework/compat.py
index 45ac49841..168bccf83 100644
--- a/rest_framework/compat.py
+++ b/rest_framework/compat.py
@@ -275,6 +275,14 @@ except ImportError:
     def pygments_css(style):
         return None
 
+
+try:
+    import pytz
+    from pytz.exceptions import InvalidTimeError
+except ImportError:
+    InvalidTimeError = Exception
+
+
 # `separators` argument to `json.dumps()` differs between 2.x and 3.x
 # See: http://bugs.python.org/issue22767
 if six.PY3:
@@ -339,6 +347,7 @@ def set_many(instance, field, value):
         field = getattr(instance, field)
         field.set(value)
 
+
 def include(module, namespace=None, app_name=None):
     from django.conf.urls import include
     if django.VERSION < (1,9):
diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index bfb24555d..41d6105ca 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -33,7 +33,8 @@ from django.utils.translation import ugettext_lazy as _
 
 from rest_framework import ISO_8601
 from rest_framework.compat import (
-    get_remote_field, unicode_repr, unicode_to_repr, value_from_object
+    InvalidTimeError, get_remote_field, unicode_repr, unicode_to_repr,
+    value_from_object
 )
 from rest_framework.exceptions import ErrorDetail, ValidationError
 from rest_framework.settings import api_settings
@@ -1087,6 +1088,7 @@ class DateTimeField(Field):
     default_error_messages = {
         'invalid': _('Datetime has wrong format. Use one of these formats instead: {format}.'),
         'date': _('Expected a datetime but got a date.'),
+        'make_aware': _('Invalid datetime for the timezone "{timezone}".')
     }
     datetime_parser = datetime.datetime.strptime
 
@@ -1107,7 +1109,10 @@ class DateTimeField(Field):
         field_timezone = getattr(self, 'timezone', self.default_timezone())
 
         if (field_timezone is not None) and not timezone.is_aware(value):
-            return timezone.make_aware(value, field_timezone)
+            try:
+                return timezone.make_aware(value, field_timezone)
+            except InvalidTimeError:
+                self.fail('make_aware', timezone=field_timezone)
         elif (field_timezone is None) and timezone.is_aware(value):
             return timezone.make_naive(value, utc)
         return value
diff --git a/tests/test_fields.py b/tests/test_fields.py
index 16221d4cc..968c41d3f 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -12,7 +12,7 @@ from django.utils import six
 from django.utils.timezone import utc
 
 import rest_framework
-from rest_framework import serializers
+from rest_framework import compat, serializers
 from rest_framework.fields import is_simple_callable
 
 try:
@@ -1205,6 +1205,30 @@ class TestNaiveDateTimeField(FieldValues):
     field = serializers.DateTimeField(default_timezone=None)
 
 
+class TestNaiveDayLightSavingTimeTimeZoneDateTimeField(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:
+        @staticmethod
+        def localize(value, is_dst):
+            raise compat.InvalidTimeError()
+
+        def __str__(self):
+            return 'America/New_York'
+
+    field = serializers.DateTimeField(default_timezone=MockTimezone())
+
+
 class TestTimeField(FieldValues):
     """
     Valid and invalid values for `TimeField`.