Connor Townsend fired Albion into the FA Cup Fifth Round after hammering home his first Baggies goal at West Ham.
The attacking full back powered in an 18-yard drive in the ninth minute at The London Stadium as Slaven Bilic marked his return to West Ham with a victory.
Championship leaders West Brom dominated their Premier League rivals for long periods and Charlie Austin and the impressive Filip Krovinovic both came close to extending Albion's league with headers.
Slaven Bilic marked his return to East London with 8 changes to the side which had lost on Monday night to Stoke at The Hawthorns.
Jonathan Bond, Semi Ajayi, Dara O'Shea, Chris Brunt, Gareth Barry, Kyle Edwards, Charlie Austin and Krovinovic were all recalled for the starting XI for the fourth round tie.
Backed by more than 5,000 travelling fans, Albion impressed and Kyle Edwards forced Darren Randolph into the first save of the game early on.
After Townsend's rocket, Albion pushed for a second with Charlie Austin wasting the visitor's best effort when he somehow headed wide unmarked on the penalty spot after a smart cross from O'Shea.
West Ham pressed for an equaliser after the break but Bond was rarely troubled in the second half, despite Semi Ajayi seeing red for two dubious cautions.