diff --git a/AUTHORS b/AUTHORS
index 460bb9a7df..87011bf1e8 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -384,6 +384,7 @@ answer newbie questions, and generally made Django that much better:
     James Bennett <james@b-list.org>
     James Murty
     James Tauber <jtauber@jtauber.com>
+    James Timmins <jameshtimmins@gmail.com>
     James Wheare <django@sparemint.com>
     Jannis Leidel <jannis@leidel.info>
     Janos Guljas
diff --git a/django/db/models/lookups.py b/django/db/models/lookups.py
index 105dc93251..2683d8971a 100644
--- a/django/db/models/lookups.py
+++ b/django/db/models/lookups.py
@@ -262,9 +262,9 @@ class Exact(FieldGetDbPrepValueMixin, BuiltinLookup):
         from django.db.models.sql.query import Query
         if isinstance(self.rhs, Query):
             if self.rhs.has_limit_one():
-                # The subquery must select only the pk.
-                self.rhs.clear_select_clause()
-                self.rhs.add_fields(['pk'])
+                if not self.rhs.has_select_fields:
+                    self.rhs.clear_select_clause()
+                    self.rhs.add_fields(['pk'])
             else:
                 raise ValueError(
                     'The QuerySet value for an exact lookup must be limited to '
diff --git a/tests/lookup/tests.py b/tests/lookup/tests.py
index a603824c0d..1958b995b2 100644
--- a/tests/lookup/tests.py
+++ b/tests/lookup/tests.py
@@ -5,6 +5,7 @@ from operator import attrgetter
 
 from django.core.exceptions import FieldError
 from django.db import connection
+from django.db.models import Max
 from django.db.models.expressions import Exists, OuterRef
 from django.db.models.functions import Substr
 from django.test import TestCase, skipUnlessDBFeature
@@ -956,3 +957,15 @@ class LookupTests(TestCase):
             ),
         )
         self.assertEqual(qs.get(has_author_alias_match=True), tag)
+
+    def test_exact_query_rhs_with_selected_columns(self):
+        newest_author = Author.objects.create(name='Author 2')
+        authors_max_ids = Author.objects.filter(
+            name='Author 2',
+        ).values(
+            'name',
+        ).annotate(
+            max_id=Max('id'),
+        ).values('max_id')
+        authors = Author.objects.filter(id=authors_max_ids[:1])
+        self.assertEqual(authors.get(), newest_author)