diff --git a/django/db/backends/base/base.py b/django/db/backends/base/base.py
index f186e3b10b..fcafa5f71a 100644
--- a/django/db/backends/base/base.py
+++ b/django/db/backends/base/base.py
@@ -88,6 +88,13 @@ class BaseDatabaseWrapper(object):
         # is called?
         self.run_commit_hooks_on_set_autocommit_on = False
 
+    def ensure_timezone(self):
+        """
+        Ensure the connection's timezone is set to `self.timezone_name` and
+        return whether it changed or not.
+        """
+        return False
+
     @cached_property
     def timezone(self):
         """
diff --git a/django/db/backends/postgresql/base.py b/django/db/backends/postgresql/base.py
index 8819c39d31..90f28703af 100644
--- a/django/db/backends/postgresql/base.py
+++ b/django/db/backends/postgresql/base.py
@@ -192,17 +192,21 @@ class DatabaseWrapper(BaseDatabaseWrapper):
 
         return connection
 
+    def ensure_timezone(self):
+        self.ensure_connection()
+        conn_timezone_name = self.connection.get_parameter_status('TimeZone')
+        timezone_name = self.timezone_name
+        if timezone_name and conn_timezone_name != timezone_name:
+            with self.connection.cursor() as cursor:
+                cursor.execute(self.ops.set_time_zone_sql(), [timezone_name])
+            return True
+        return False
+
     def init_connection_state(self):
         self.connection.set_client_encoding('UTF8')
 
-        conn_timezone_name = self.connection.get_parameter_status('TimeZone')
-
-        if self.timezone_name and conn_timezone_name != self.timezone_name:
-            cursor = self.connection.cursor()
-            try:
-                cursor.execute(self.ops.set_time_zone_sql(), [self.timezone_name])
-            finally:
-                cursor.close()
+        timezone_changed = self.ensure_timezone()
+        if timezone_changed:
             # Commit after setting the time zone (see #17062)
             if not self.get_autocommit():
                 self.connection.commit()
diff --git a/django/test/signals.py b/django/test/signals.py
index 62b386268c..70b20625ff 100644
--- a/django/test/signals.py
+++ b/django/test/signals.py
@@ -69,10 +69,7 @@ def update_connections_time_zone(**kwargs):
                 del conn.timezone_name
             except AttributeError:
                 pass
-            tz_sql = conn.ops.set_time_zone_sql()
-            if tz_sql and conn.timezone_name:
-                with conn.cursor() as cursor:
-                    cursor.execute(tz_sql, [conn.timezone_name])
+            conn.ensure_timezone()
 
 
 @receiver(setting_changed)