The Black Cats fell a goal behind on the stroke of half-time when Luke O’Nien conceded a penalty and John Swift converted from the spot.
Yet two second-half goals from Dennis Cirkin saw the visitors turn the game around, with the second coming six minutes from time.
The result moves the Black Cats up to sixth in the Championship table with two games remaining.
Here’s how Phil Smith rated the Sunderland players against West Brom:
1. Anthony Patterson - 7
Despite the odd uncertain moment his distribution was good and calm. Had very little to do in terms of saves to make. 7 Photo: Martin Swinney
2. Trai Hume - 7
Had a really good game, winning a lot of headers and keeping it simple in possession on the right of a back three. 7 Photo: Frank Reid
3. Luke O’Nien - 7
Was excellent on the ball throughout, in what was a crucial role in an unorthodox defence due to injury. One or two rash moments but given the circumstances, a big performance. 7 Photo: Frank Reid
4. Dennis Cirkin - 9
One of the best and most unlikely of Sunderland braces. His header for the first was excellent and though the second took a deflection, he was rewarded again for getting into a dangerous area. Now has five goals for the season. 9 Photo: Frank Reid