Wayne Rooney's ninth-minute goal was enough for Sir Alex Ferguson's men to tee up a fourth round meeting at home with Fulham but it could have been a more comfortable win if the England striker had not missed a penalty with 10 minutes remaining.
United skipped away to an early lead when Javier Hernandez ran onto a clever through ball from Anderson before squaring for Rooney to finish with a sliding tap-in before paying respect to his late sister-in-law by raising his hands to the sky.
West Ham did manage to rally slightly in the second half with some controlling play but United were awarded a penalty when Ryan Giggs' cross was adjudged to have been handled in the area by Jordan Spence with Rooney stepping up. The effort was a wayward one, going well wide of the mark, and making it five misses from the spot this season for United.
However, the damage had already been done as the home side achieved the required result that keeps them alive in the cup whilst West Ham are forced to focus on a top-half finish in the league.
2012/13 FA Cup third round replay
Old Trafford, Manchester - 71,081