Goals from Manuel Lanzini and Jarrod Bowen saw West Ham overcome Premier League rivals Leeds and into the FA Cup fourth round.
Lanzini forced home the opener from close range after Nikola Vlasic had been denied by Illan Meslier.
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The impressive Bowen then sealed the tie in the final minute of stoppage-time from Michail Antonio’s pass.
Leeds went close through Jack Harrison and and Dan James late on, but could not force their efforts on target.