diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 103fffa47d..9865e88fd0 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -1087,7 +1087,12 @@ class Query(BaseExpression):
         if select:
             self.append_annotation_mask([alias])
         else:
-            self.set_annotation_mask(set(self.annotation_select).difference({alias}))
+            annotation_mask = (
+                value
+                for value in dict.fromkeys(self.annotation_select)
+                if value != alias
+            )
+            self.set_annotation_mask(annotation_mask)
         self.annotations[alias] = annotation
 
     def resolve_expression(self, query, *args, **kwargs):
@@ -2341,12 +2346,12 @@ class Query(BaseExpression):
         if names is None:
             self.annotation_select_mask = None
         else:
-            self.annotation_select_mask = set(names)
+            self.annotation_select_mask = list(dict.fromkeys(names))
         self._annotation_select_cache = None
 
     def append_annotation_mask(self, names):
         if self.annotation_select_mask is not None:
-            self.set_annotation_mask(self.annotation_select_mask.union(names))
+            self.set_annotation_mask((*self.annotation_select_mask, *names))
 
     def set_extra_mask(self, names):
         """
@@ -2423,9 +2428,9 @@ class Query(BaseExpression):
             return {}
         elif self.annotation_select_mask is not None:
             self._annotation_select_cache = {
-                k: v
-                for k, v in self.annotations.items()
-                if k in self.annotation_select_mask
+                k: self.annotations[k]
+                for k in self.annotation_select_mask
+                if k in self.annotations
             }
             return self._annotation_select_cache
         else:
diff --git a/docs/releases/5.0.txt b/docs/releases/5.0.txt
index 385f4a6512..b2e8b9d48b 100644
--- a/docs/releases/5.0.txt
+++ b/docs/releases/5.0.txt
@@ -295,6 +295,9 @@ Miscellaneous
 * Integer fields are now validated as 64-bit integers on SQLite to match the
   behavior of ``sqlite3``.
 
+* The undocumented ``Query.annotation_select_mask`` attribute is changed from a
+  set of strings to an ordered list of strings.
+
 .. _deprecated-features-5.0:
 
 Features deprecated in 5.0
diff --git a/tests/postgres_tests/test_array.py b/tests/postgres_tests/test_array.py
index f7615c974e..5f8441ba1b 100644
--- a/tests/postgres_tests/test_array.py
+++ b/tests/postgres_tests/test_array.py
@@ -466,8 +466,8 @@ class TestQuerying(PostgreSQLTestCase):
                 ],
             )
         sql = ctx[0]["sql"]
-        self.assertIn("GROUP BY 1", sql)
-        self.assertIn("ORDER BY 1", sql)
+        self.assertIn("GROUP BY 2", sql)
+        self.assertIn("ORDER BY 2", sql)
 
     def test_index(self):
         self.assertSequenceEqual(
diff --git a/tests/queries/test_qs_combinators.py b/tests/queries/test_qs_combinators.py
index bf127ce703..71d2418f2b 100644
--- a/tests/queries/test_qs_combinators.py
+++ b/tests/queries/test_qs_combinators.py
@@ -246,7 +246,7 @@ class QuerySetSetOperationTests(TestCase):
             )
             .values_list("num", "count")
         )
-        self.assertCountEqual(qs1.union(qs2), [(1, 0), (2, 1)])
+        self.assertCountEqual(qs1.union(qs2), [(1, 0), (1, 2)])
 
     def test_union_with_extra_and_values_list(self):
         qs1 = (
@@ -368,6 +368,20 @@ class QuerySetSetOperationTests(TestCase):
             [reserved_name.pk],
         )
 
+    def test_union_multiple_models_with_values_list_and_annotations(self):
+        ReservedName.objects.create(name="rn1", order=10)
+        Celebrity.objects.create(name="c1")
+        qs1 = ReservedName.objects.annotate(row_type=Value("rn")).values_list(
+            "name", "order", "row_type"
+        )
+        qs2 = Celebrity.objects.annotate(
+            row_type=Value("cb"), order=Value(-10)
+        ).values_list("name", "order", "row_type")
+        self.assertSequenceEqual(
+            qs1.union(qs2).order_by("order"),
+            [("c1", -10, "cb"), ("rn1", 10, "rn")],
+        )
+
     def test_union_in_subquery(self):
         ReservedName.objects.bulk_create(
             [