Stoke had midfielders Ibrahim Afellay and Charlie Adam sent off as West Brom secured a first league win this season.
Afellay went for reacting to a challenge by Craig Gardner before Adam followed six minutes later after appearing to stamp on Craig Dawson.
West Brom took the lead when club record £12m signing Salomon Rondon headed home Rickie Lambert’s cross.
It was enough to earn Baggies boss Tony Pulis victory on his first return to his former club.
Pulis was given a standing ovation by a sell-out crowd at Stoke, the club he took into the Premier League, and led to the 2011 FA Cup final and a place in the Europa League.
ut home fans were not so generous towards referee Michael Oliver as the hosts were left to play with nine men for more than an hour.