Salomon Rondon scored in first half stoppage time to take the spoils in a controversial match that saw the hosts finish with nine-men.
The game marked the return of Tony Pulis back to the Britannia Stadium and it saw him record a third win against his former employers in three games.
Xherdan Shaqiri made his home debut for the Potters while Charlie Adam deputised in place of Marko Arnautovic in Mark Hughes’ only change.
Stoke zipped the ball around well in the early stages, keeping possession well but rarely seeing a sight of the West Brom goal. Mame Diouf saw his header straight into the arms of a grateful Boaz Myhill.
An early flashpoint saw Ibrahim Afellay bundled over the hoardings with the ball out of play. The Dutchman reacted angrily only to be spoken to from Michael Oliver.
James Morrison stung the palms of Jack Butland, who got down well to his right to stop a well struck shot while Stoke were reduced to shots from distance.
The first red card saw Afellay breaking from a West Brom corner only to be cynically stopped by Craig Gardner. Afellay bounced up and put his hand in Gardner’s face, which saw the Stoke player dismissed.
Just six minutes later Charlie Adam was dismissed. The Scotland international went into a tackle with Craig Dawson for assistant referee to call something to Oliver’s attention, which resulted in the second red card.
With the two-man advantage, Pulis brought on Rickie Lambert for defensive midfielder Claudio Yacob in an attempt to go for the jugular.
Then in stoppage time came the only goal of the game when Lambert’s cross was met by record signing Salomon Rondon, whose header snuck in at the far post past a helpless Butland.
There were few chances to note in the second half with Stoke trying to keep possession. The Baggies failed to utilise the space available and Stoke nearly made them pay.
In stoppage time Stoke won a free-kick on the edge of the box but Marko Arnautovic could only find the wall with the initial effort before putting the rebound in the Boothen End.
Mark Hughes told BBC Radio Stoke: “The referee hasn’t looked after the game. He hasn’t shown any common sense really.
“We were so clearly the dominant team in the opening stages. It was only a matter of time before we created a chance but unfortunately the referee only saw one side of the coin with the Afellay red card.
“He raised his hands, which is a sending off. But you have to see the whole incident. He reacted to Craig Gardner raising his hands towards him.
“The second one Charlie [Adam] has done well to block the cross. The lads followed through and wrapped his legs around Charlie [Adam]. As he’s unbalanced his stepped on him. It wasn’t a stamp. The referee needs to be strong and oversee his assistant, who sprinted over.”
On the performance he added: “The way we kept going and stayed in the game and Stoke created chances showed great credit. I was really proud but we come away with nothing.
“It was clear in the first 20-25 minutes, West Brom didn’t string two passes together and it was a matter of time. It was taken away from us unfortunately.
Stoke: Butland, Johnson (Wilson), Muniesa, Cameron, Pieters, Whelan, Van Ginkel, Afellay, Adam, Shaqiri (Arnautovic), Diouf (Ireland)
West Brom: Myhill, Lescott, McAuley, Olsson, Dawson, Yacob (Lambert), Morrison, McClean (McManaman), Gardner (Gamboa), Fletcher, Rondon
Referee: Michael Oliver
Man of the Match: Glenn Whelan