The win has moved Stoke into 14th position in the Premier League table, while West Brom remain 19th as the Baggies made it 17 games without a win in the top flight.
Rondon could have levelled the scores in the 30th minute after finding himself all alone inside the home side's box, but the striker, who appeared to think he was offside, missed the goal once again.
The West Brom response was strong as Alan Pardew's side looked to hit back in the latter stages of the first period, but Stoke doubled their lead in the second minute of stoppage time when Eric Maxim Choupo-Moting took advantage of a poor back-pass from Gareth Barry before finishing past Foster.
West Brom had one back early in the second half, however, when Rondon, who had missed a couple of brilliant chances in the first period, raced onto a through-pass from Chris Brunt before finishing into the back of the net.
Jake Livermore had a decent chance to level the scores 20 minutes from time after finding space on the edge of the box, but the midfielder missed the target.
Jonny Evans also came close with a couple of headers for the visitors in the latter stages, but 2-1 Stoke was how the score stayed entering the final 10 minutes of football.
West Brom continued to pour players forward in the latter stages in a bid to level, but it was Stoke that grabbed a third in the fifth minute of added time at the end of the 90 when Ramadan Sobhi netted from close range after a pass from Choupo-Moting.
Stoke (5-4-1): Butland; Edwards, Wimmer, Zouma, Shawcross, Cameron; Shaqiri (Sobhi 79'), Allen, Fletcher (Diouf 67'), Choupo-Moting; Crouch
West Brom (4-2-3-1): Foster, Nyom, Evans, Hegazi, Gibbs (Burke 81'); Livermore, Barry; McClean (Chadli 46', Rodriguez 61'), Robson-Kanu, Brunt; Rondon