Albion have had a half to forget at the London Stadium.
Jeremy Sarmiento and Adam Webster both limped off injured.
Solly March and Shane Duffy came on as substitutes.
Five minutes into the game, Tomas Soucek scored for the Hammers after a perfect delivery from a corner taken by Pablo Fornals.
It left Robert Sanchez flapping around almost inside his goal.
Two minutes earlier, Neal Maupay scuffed a close-range chance wide after great work from Jakub Moder.
Lewis Dunk and Moder have also had clear chances for Albion.
And Fornals cracked an effort against the bar for West Ham.
