diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index bb230647eb..f8e146b8de 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -2155,6 +2155,15 @@ class Query(BaseExpression):
             # SELECT clause which is about to be cleared.
             self.set_group_by(allow_aliases=False)
             self.clear_select_fields()
+        elif self.group_by:
+            # Resolve GROUP BY annotation references if they are not part of
+            # the selected fields anymore.
+            group_by = []
+            for expr in self.group_by:
+                if isinstance(expr, Ref) and expr.refs not in field_names:
+                    expr = self.annotations[expr.refs]
+                group_by.append(expr)
+            self.group_by = tuple(group_by)
 
         self.values_select = tuple(field_names)
         self.add_fields(field_names, True)
diff --git a/docs/releases/3.0.7.txt b/docs/releases/3.0.7.txt
index 9fc71d9aa2..5457e59b3d 100644
--- a/docs/releases/3.0.7.txt
+++ b/docs/releases/3.0.7.txt
@@ -11,3 +11,7 @@ Bugfixes
 
 * Fixed a regression in Django 3.0 by restoring the ability to use field
   lookups in ``Meta.ordering`` (:ticket:`31538`).
+
+* Fixed a regression in Django 3.0 where ``QuerySet.values()`` and
+  ``values_list()`` crashed if a queryset contained an aggregation and a
+  subquery annotation (:ticket:`31566`).
diff --git a/tests/annotations/tests.py b/tests/annotations/tests.py
index db4413564c..dad34e03eb 100644
--- a/tests/annotations/tests.py
+++ b/tests/annotations/tests.py
@@ -1,10 +1,13 @@
 import datetime
 from decimal import Decimal
+from unittest import skipIf
 
 from django.core.exceptions import FieldDoesNotExist, FieldError
+from django.db import connection
 from django.db.models import (
-    BooleanField, CharField, Count, DateTimeField, ExpressionWrapper, F, Func,
-    IntegerField, NullBooleanField, OuterRef, Q, Subquery, Sum, Value,
+    BooleanField, CharField, Count, DateTimeField, Exists, ExpressionWrapper,
+    F, Func, IntegerField, Max, NullBooleanField, OuterRef, Q, Subquery, Sum,
+    Value,
 )
 from django.db.models.expressions import RawSQL
 from django.db.models.functions import Length, Lower
@@ -619,3 +622,16 @@ class NonAggregateAnnotationTestCase(TestCase):
             total_books=Subquery(long_books_qs, output_field=IntegerField()),
         ).values('name')
         self.assertCountEqual(publisher_books_qs, [{'name': 'Sams'}, {'name': 'Morgan Kaufmann'}])
+
+    @skipIf(connection.vendor == 'oracle', 'See https://code.djangoproject.com/ticket/31584')
+    def test_annotation_exists_aggregate_values_chaining(self):
+        qs = Book.objects.values('publisher').annotate(
+            has_authors=Exists(Book.authors.through.objects.filter(book=OuterRef('pk'))),
+            max_pubdate=Max('pubdate'),
+        ).values_list('max_pubdate', flat=True).order_by('max_pubdate')
+        self.assertCountEqual(qs, [
+            datetime.date(1991, 10, 15),
+            datetime.date(2008, 3, 3),
+            datetime.date(2008, 6, 23),
+            datetime.date(2008, 11, 3),
+        ])