diff --git a/google/auth/transport/requests.py b/google/auth/transport/requests.py
index a4784b3..817176b 100644
--- a/google/auth/transport/requests.py
+++ b/google/auth/transport/requests.py
@@ -340,17 +340,19 @@
         self._default_host = default_host
 
         if auth_request is None:
-            auth_request_session = requests.Session()
+            self._auth_request_session = requests.Session()
 
             # Using an adapter to make HTTP requests robust to network errors.
             # This adapter retrys HTTP requests when network errors occur
             # and the requests seems safely retryable.
             retry_adapter = requests.adapters.HTTPAdapter(max_retries=3)
-            auth_request_session.mount("https://", retry_adapter)
+            self._auth_request_session.mount("https://", retry_adapter)
 
             # Do not pass `self` as the session here, as it can lead to
             # infinite recursion.
-            auth_request = Request(auth_request_session)
+            auth_request = Request(self._auth_request_session)
+        else:
+            self._auth_request_session = None
 
         # Request instance used by internal methods (for example,
         # credentials.refresh).
@@ -533,3 +535,8 @@
     def is_mtls(self):
         """Indicates if the created SSL channel is mutual TLS."""
         return self._is_mtls
+
+    def close(self):
+        if self._auth_request_session is not None:
+            self._auth_request_session.close()
+        super(AuthorizedSession, self).close()
diff --git a/system_tests/system_tests_sync/test_requests.py b/system_tests/system_tests_sync/test_requests.py
index 3ac9179..2800484 100644
--- a/system_tests/system_tests_sync/test_requests.py
+++ b/system_tests/system_tests_sync/test_requests.py
@@ -32,8 +32,10 @@
 
     # List Pub/Sub Topics through the REST API
     # https://cloud.google.com/pubsub/docs/reference/rest/v1/projects.topics/list
-    response = session.get("https://pubsub.googleapis.com/v1/projects/{}/topics".format(project_id))
-    response.raise_for_status()
+    url = "https://pubsub.googleapis.com/v1/projects/{}/topics".format(project_id)
+    with session:
+        response = session.get(url)
+        response.raise_for_status()
 
     # Check that self-signed JWT was created and is being used
     assert credentials._jwt_credentials is not None
diff --git a/tests/transport/test_requests.py b/tests/transport/test_requests.py
index f494c14..ed9300d 100644
--- a/tests/transport/test_requests.py
+++ b/tests/transport/test_requests.py
@@ -213,7 +213,7 @@
             mock.sentinel.credentials, auth_request=auth_request
         )
 
-        assert authed_session._auth_request == auth_request
+        assert authed_session._auth_request is auth_request
 
     def test_request_default_timeout(self):
         credentials = mock.Mock(wraps=CredentialsStub())
@@ -504,3 +504,22 @@
         auth_session.configure_mtls_channel(mock_callback)
         assert not auth_session.is_mtls
         mock_callback.assert_not_called()
+
+    def test_close_wo_passed_in_auth_request(self):
+        authed_session = google.auth.transport.requests.AuthorizedSession(
+            mock.sentinel.credentials
+        )
+        authed_session._auth_request_session = mock.Mock(spec=["close"])
+
+        authed_session.close()
+
+        authed_session._auth_request_session.close.assert_called_once_with()
+
+    def test_close_w_passed_in_auth_request(self):
+        http = mock.create_autospec(requests.Session)
+        auth_request = google.auth.transport.requests.Request(http)
+        authed_session = google.auth.transport.requests.AuthorizedSession(
+            mock.sentinel.credentials, auth_request=auth_request
+        )
+
+        authed_session.close()  # no raise