The same player missed a second-half penalty to ensure that West Ham remained in the tie, but the visitors could not find the important equaliser to force extra time.
It was not a classic by any means, but both sides had chances, although it was to be United who moved on to face Fulham in the next round.
Sports Mole analyses below all the action from the third round replay at Old Trafford.
On target 6
On target 4
Was the result fair?
Yes, West Ham can have no complaints. Although both sides did have chances, by far the better ones fell to the home side and the best two of the lot both went to Rooney. He finished the first after being set up by Hernandez but blazed a penalty over the bar.
Man United's performance
Good enough. With 10 changes it was never likely to be a fluid United display and it wasn't. However, they created enough and dominated for long enough periods that Alex Ferguson will be delighted that he didn't need to call upon the services of Robin van Persie from the bench.
West Ham's performance
They just didn't create enough throughout to have deserved anything from the game. In the first half they were outplayed and, despite being much better after the break, once Carlton Cole was subbed off there was not much attacking threat. Anders Lindegaard did not have any real saves to make.
Sports Mole's man of the match
Ryan Giggs: In a game without many standout performers, Giggs takes this award with a typical battling display. There's no doubt without the Welshman captaining the side today United would have been a lot less comfortable.
Had Phil Dowd's poor decision to award a harsh penalty for handball or Rooney's miss from that kick mattered, this might have gone to either of them. As it is, Tomkins is given it for his decision to try to play Javier Hernandez offside from Anderson's pass for the only goal. He was too late stepping up and, although very marginal, the goal ultimately settled the contest.
Dowd had an excellent game up until the awarding of the penalty. His bookings were all fair and there were no controversial calls until he penalised Jordan Spence for handball. The defender was running – and you need your arms to run – with no intention to touch the ball whatsoever. Fortunately for Dowd, Rooney skied the spot kick.
Man United: The Red Devils have a tricky league fixture away to Tottenham Hotspur on Sunday. However, that they got through tonight with some big names rested will help come the weekend.
West Ham: West Ham return to Upton Park on Saturday and host fellow Londoners Queens Park Rangers in an important clash in the bottom half of the Premier League.