And it could have been worse for the Gunners had Delap managed to get a little more power on a goalbound header that Clichy cleared.
A tame Emmanuel Adebayor shot that Sorensen comfortably gathered was the best Arsenal could muster.
The Gunners brought on Walcott on 57 minutes in the hope of adding some thrust to their play.
But with Cesc Fabregas a shadow of himself, one wondered where the England youngster's supply line would come from.
Instead it was the hosts who almost scored when another Delap throw caused mayhem and Salif Diao's volley from the edge of the area was superbly saved by Almunia.
I'm not all Stoke have got - Delap
It was a warning that Arsenal failed to heed, and from Delap's next throw-in, Ryan Shawcross nodded on and Olofinjana scrambled the ball over the line, nudging it forwards twice with his chest.
Worse was to come on a miserable day for the visitors when Van Persie, on the pitch for only 12 minutes, was dismissed after needlessly barging into Sorensen.
And boss Arsene Wenger could also be without three other first-teamers in the coming weeks because of injuries. Walcott was stretchered off with a shoulder problem, while Adebayor and Bacary Sagna also left the field with knocks.
Clichy's late effort from the edge of the box went in with the help of a couple of deflections.
But there was to be no great escape for Arsenal, and they would not have deserved one.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.