The home side led 1-0 at the interval following a close-range finish from Saido Berahino.
Both teams had a number of opportunities in an end-to-end second period, but West Ham could not respond as the Baggies eased their relegation worries with a vital three points.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
WEST BROM: Foster; Reid, Dawson, Olsson, Jones; Amalfitano, Mulumbu, Dorrans, Brunt; Sessegnon; Berahino
WEST HAM: Adrian; Demel, Tomkins, Reid, McCartney; Nolan, Noble, Diame; Jarvis, Carroll, Downing