diff --git a/src/flask/app.py b/src/flask/app.py
index 652b9bbf71..f32d44e142 100644
--- a/src/flask/app.py
+++ b/src/flask/app.py
@@ -721,7 +721,9 @@ def run(
         sn_host = sn_port = None
 
         if server_name:
-            sn_host, _, sn_port = server_name.partition(":")
+            sn_host, _, sn_port = server_name.rpartition(":")
+            if not _:
+                sn_host, sn_port = sn_port, None
 
         if not host:
             if sn_host:
diff --git a/src/flask/testing.py b/src/flask/testing.py
index 68b1ab48c6..89590e9d96 100644
--- a/src/flask/testing.py
+++ b/src/flask/testing.py
@@ -177,7 +177,7 @@ def session_transaction(
             app.session_interface.save_session(app, sess, resp)
 
         self._update_cookies_from_response(
-            ctx.request.host.partition(":")[0],
+            ctx.request.host.rpartition(":")[0] or ctx.request.host,
             ctx.request.path,
             resp.headers.getlist("Set-Cookie"),
         )