Viktor Gyokeres' stoppage-time penalty sent Coventry City up to eighth in the Championship and ended West Bromwich Albion's five-game winning run.
Gyokeres, the division's leading scorer, was fouled in the box and sent Alex Palmer the wrong way from the spot for his 11th goal of the season.
Before then, the Sky Blues had come closest to a winning goal when Jonathan Panzo headed against the crossbar.
Victory took the home side to within one point of the play-off places.
Coventry had the better of a goalless first half, showing little sign of a hangover after surrendering a three-goal lead against Swansea on Saturday.