diff --git a/django/db/models/query.py b/django/db/models/query.py
index 811e917764..9dcf620448 100644
--- a/django/db/models/query.py
+++ b/django/db/models/query.py
@@ -274,9 +274,12 @@ class QuerySet(object):
 
         query = self.query.clone()
 
+        aggregate_names = []
         for (alias, aggregate_expr) in kwargs.items():
             query.add_aggregate(aggregate_expr, self.model, alias,
-                is_summary=True)
+                                is_summary=True)
+            aggregate_names.append(alias)
+        query.append_aggregate_mask(aggregate_names)
 
         return query.get_aggregation(using=self.db)
 
diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 2a9b8ef826..da0c39e1e7 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -1753,6 +1753,10 @@ class Query(object):
             self.aggregate_select_mask = set(names)
         self._aggregate_select_cache = None
 
+    def append_aggregate_mask(self, names):
+        if self.aggregate_select_mask is not None:
+            self.set_aggregate_mask(set(names).union(self.aggregate_select_mask))
+
     def set_extra_mask(self, names):
         """
         Set the mask of extra select items that will be returned by SELECT,
diff --git a/tests/aggregation/tests.py b/tests/aggregation/tests.py
index c635e6ebb6..dd7e994a63 100644
--- a/tests/aggregation/tests.py
+++ b/tests/aggregation/tests.py
@@ -585,3 +585,14 @@ class BaseAggregateTestCase(TestCase):
                 "datetime.date(2008, 1, 1)"
             ]
         )
+
+    def test_values_aggregation(self):
+        # Refs #20782
+        max_rating = Book.objects.values('rating').aggregate(max_rating=Max('rating'))
+        self.assertEqual(max_rating['max_rating'], 5)
+        max_books_per_rating = Book.objects.values('rating').annotate(
+            books_per_rating=Count('id')
+        ).aggregate(Max('books_per_rating'))
+        self.assertEqual(
+            max_books_per_rating,
+            {'books_per_rating__max': 3})