Stoke maintained their unbeaten start to the season as Ryan Shotton poached a goal in the last minute to consign West Brom to their third straight defeat.
Shotton pipped Ben Foster to the ball to tap home with the West Brom keeper claiming he had both hands on it.
Shane Long had the Baggies best chance of the game but saw his diving header expertly kept out by the impressive Asmir Begovic in the Stoke goal.
Jermaine Pennant also went close for Stoke, heading just wide.
The result was desperately harsh on West Brom who had been the better team throughout with Stoke managing just one effort on target in the entire game.
But despite their endeavour Roy Hodgson's side are still searching for their first points of the campaign and sit alongside Tottenham and Blackburn in the bottom three without a point.
West Brom started brightly and full of intent but found Stoke keeper Begovic in fine form.
Paul Scharner was the first man to test the big Bosnian with a header straight at Begovic, before an unmarked Chris Brunt then headed wide from Somen Tchoyi's cross and really should have done better.
A few moments later Stoke were again saved by Begovic.
Tchoyi was again the provider, this time marauding down the left wing, but Long's diving header from 10 yards was superbly kept out by Begovic's point-blank save.
Brunt then curled a free-kick wide of the post but as the half wore on the game lost its way, with Stoke missing their usual intensity.
The arrival of a first-half downpour did little to help the pace of the game or indeed the muted atmosphere inside the Hawthorns but Stoke did at least manage one decent effort with Pennant heading Matthew Etherington's cross just wide of the angle.
Kenywne Jones, who had been anonymous in the first half, was then lucky to escape punishment for a late stamp on Steven Reid while Glenn Whealan toe poked just wide from 18 yards.
Tchoyi, the most lively player on the pitch, turned his marker well on the edge of the area but curled his effort wide of Begovic's post.
Tchoyi then volleyed wide from just inside the box before being replaced by Marc-Antoine Fortune as the game looked to be heading for a draw.
But with only injury time left Shotton showed great persistence in chasing a long ball and with Foster about to collect the ball he pinched it from his grasp following a mix up with centre-back Gabriel Tamas before tapping into an empty net from close range to push Stoke up to ninth.
West Brom manager Roy Hodgson
"To lose like that is very galling especially having seen the replays. I thought we defended it very, very badly.
"Foster could have been brave and taken the stud in the chest.
"But unfortunately he decided to turn away from the stud and, as a result, we conceded a goal.
"I think the referee could have helped in the situation by giving the free-kick because the player has put his foot high and was leading with his studs.
"I saw it as a foul, the ref didn't. That is football."
Stoke City manager Tony Pulis
"If we got a decision go our way, then fine. During this season, we will have a lot go against us.
"It all evens itself up. If we got away with one, it is bad luck for Roy and good luck for us and Stoke.
"But I thought it was a goal. I don't think Ryan caught the 'keeper at all.
"To be honest, I didn't look at the linesman thinking it was going to be a free-kick."