Having seen leaders Leeds draw with lowly Luton on Tuesday, the Baggies took the lead against Wednesday through a Charlie Austin penalty.
Matheus Pereira scored twice in the second half to ensure the win and move a point behind Leeds and five ahead of third-placed Brentford.
Derby beat play-off rivals Preston 1-0 thanks to Wayne Rooney’s 18th-minute free-kick.
The result sees Derby close the gap on sixth-placed Cardiff to a point, while Preston are four points outside the play-off places.
Huddersfield moved out of the relegation zone with a 3-0 win at Birmingham.
Karlan Grant scored an early penalty and although he then saw another spot-kick saved after the break, Frazier Campbell soon made it 2-0. Elias Kachunga added a third in the 72nd minute.
A fine free-kick from Tiago Silva earned Nottingham Forest a 1-0 win over Bristol City that moved them up to fourth, seven points behind West Brom.
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