United controlled the first half without creating many real chances, with West Ham improving after the break but they could not grab an equaliser.
United were awarded a penalty late in the second half, but Rooney blazed the effort over the bar.
Read how the action unfolded below with Sports Mole's live commentary.
7.01pmGood evening and thanks for joining me for this FA Cup third-round replay from Old Trafford.
7.02pmTonight we will find out who gets to host Fulham in the next round of the FA Cup. The London side went through last night with a comeback win at Blackpool.
7.04pmIn the original fixture on January 5, West Ham looked set for a famous win until Robin van Persie's moment of brilliance very late on nicked Man Utd a draw and the chance of tonight's replay. For a reminder of that game, click here.
7.20pmThere is also a place for Nani and Anderson as Sir Alex Ferguson rests some first-team players but still puts out a competitive side.
7.21pmHere is our full team news, for further information.
7.25pmIn terms of previous results between these sides, Man Utd have won eight of the last 10 in all competitions. With West Ham's highly-depleted defence it will be a hard ask for them tonight. However with the FA Cup, you never know.
7.28pmIn three of the past five season West Ham have failed to reach the fourth round. They were beaten finalists in 2006 and won the tournament in 1964, 1975 and 1980.
7.31pmIn the buildup to this game, Ferguson insisted that United were looking to go all the way in the cup this season. That's despite making no fewer than 10 changes to his lineup tonight.
7.33pm"We want to try and have a go at this FA Cup," Ferguson told MUTV. "We haven't had a run for a long time, two or three years, and we have had some bad draws."
7.35pmFor the visitors, Alou Diarra has urged his teammates to improve on their showing against Sunderland.
7.37pmSpeaking to his club's official website, Diarra said: "For us, it's a question of raising our game in comparison to our performance at Sunderland and start the match just as we did in the home game."
7.39pmTonight's other replay is underway at the Emirates, where Arsenal are hosting Swansea. It's currently 0-0 in the game where the victor travels to the South Coast to face Brighton & Hove Albion.
7.44pmA quick look at the odds for tonight. The best odds you can find on a home win tonight is 1/3 - United are the overwhelming favourites. West Ham could be a good punt at 19/2 to win outright.
7.48pmI can't look beyond United tonight, despite the weakened side, and I think it could be 3-1 - that score can be backed at 11s.
7.50pmJust over 15 minutes away from kickoff. I reckon we're in for a good one. Both teams would see a home tie with Fulham as a chance to make the fifth round so will certainly be giving it their all.
7.54pmUnited have gone out at this stage just once under Ferguson, but that by no means makes it a foregone conclusion. West Ham will be a threat to their inexperienced defence.
7.59pmIt will be interesting to see how Rooney and Javier Hernandez link up today without Van Persie. They're obviously excellent players but it will be a boost for the Hammers that the Dutchman isn't started.
8pmA quick Tweet from @ whufc_official: "There will be around 1,400 West Ham United fans at Old Trafford this evening. Fantastic support, as always!"
8.01pmJust five minutes now until kickoff. With the respective defences that both managers have picked, there could be mistakes and goals and attacking will be the way to win this one.
8.03pmUPDATE: Still 0-0 in London, but former Gunner Kyle Bartley has rattled the bar with a header.
8.05pmGiggs is United's captain tonight. His experienced head will be important with some rusty legs around him - namely the returning Anderson and Nani.
0 minEarly corner here on the right for the hosts...
1 minThey go short, and Giggs's eventual cross is closed down.
3 minFirst spell of possession for West Ham, and they win a free-kick on the left after a foul from Phil Jones.
4 minUnited break from it and win another corner at the other end.
5 minSpence heads it away well to Vaz Te, but he is crowded out as he tries to break. A sloppy pass forwards gives Vaz Te a chance to find Carlton Cole, but his pass asks too much of the striker. Neither side on top of this in the opening five minutes.
6 minSHOT! A cross from Valencia is headed out to Alexander Buttner, but his strike from 25 yards is high and wide of the right-hand post.
8 minThe atmosphere is a bit flat at the moment - the away fans are certainly louder. Good chance there for Vaz Te from just outside the box but his low shot is straight at Anders Lindegaard. Matt Taylor had made an excellent run but Vaz Te delayed.
15 minUnited now passing the ball around well. Good movement in midfield creates space for Valencia to cross, but Tomkins gets a good forehead on the ball to clear it.
17 minNow it's West Ham's turn to pass it around the middle. Diame's pass was cut out by Jones, who gave it straight back, but the Senegalese then overhit a pass into the box.
18 minCole finds Diame, who burst forward and struck left-footed. It's deflected behind for a corner.
18 minFrom the corner, Giggs looks for Nani with an angled long-ball, but the Portuguese just cannot keep it in play.
20 minO'Neil pips Valencia to the ball, but is then brought down about 40 yards from goal. He'll take it himself..
22 minO'Neil this time loses out to Hernandez. Giggs looks for the Mexican over the top but this time he is offside. Just as well, as he's then clattered by Diarra.
23 minThere's not been a lot of threat from West Ham so far. Not a great deal from United either, in truth, but the one golden chance has been converted and they have been better with the ball.
25 minThis game has entered a scrappy spell. First Cole loses out, before Rooney is crowded out by five blue shirts. Then Jones lumps one out of play from the back.
26 minJones again lumps it out of play, but this time for good reason as he beat Cole to the ball to clear.
27 minUnited work it from the back. Rafael cuts inside to find Rooney, who rides a challenge from Diarra before looking for Valencia. His pass is put out for a corner, though.
28 minOFF THE LINE! The corner is again worked short, and after the cross comes in Nani hits a snap-shot towards the far bottom corner. Jaaskelainen is beaten but Dan Potts is there to clear from behind his goalkeeper.
29 minAfter that clearance Smalling got up for an unmarked header but directed it straight at Jaaskelainen. Two great chances in a minute.
30 min..It's again short to Giggs, who finds Rooney again and his cross is deep, straight to Jaaskelainen. But the 'keeper spills it, however it's cleared by an alert defence.
32 minA low driven cross by Buttner hits the base of the post and goes wide. Jaaskelainen was never in danger, he had it covered.
33 minAll the action is in the West Ham half now. They try to get away via Spence, but his touch is heavy and United come again. It's eventually a Hammers free-kick when Valencia is given offside.
35 minWest Ham work a bit of possession, but are really struggling to create anything when they near the final third. O'Neil tries to create something with a dinked ball into the box but it was an awful attempt and goes out for a goal-kick.
37 minThe United pressure has died off now and West Ham try to work another move. Diame drives through and finds Taylor, whose cross is headed clear and United deal with the threat once more without a shot on their goal.
38 minSelfish again from Nani, this time from much further out. He had Rooney to his right and Hernandez in the box but shoots high and wide from 35 yards.
40 minAnother corner on the left for United, which Rooney goes over to take.
41 minCHANCE! Reid just about beat Smalling in the air, before Taylor slices Rooney's cross. United keep the ball and Anderson finds Buttner, who works to Rooney whose shot from outside the box is saved well down to his right from Jaaskelainen.
42 minAnother cross comes in for West Ham and once more is cleared by a defensive header, this time Smalling.
44 minCHANCE! A spell of possession for United on the edge of the box. Nani finds Hernandez, who flicks on to Anderson, whose shot is blocked then comes off him for a goal-kick. Well worked.
45 minJust one minute of added-on time to be played, and we're 20 seconds into it.
8.53pmUnited are deservedly in front at the half, but West Ham are certainly still in it at just 1-0. The visitors have created next to nothing, however, and will have to improve.
8.55pmThe best chance of the game was the goal after nine minutes, with Rooney capping off a good move involving Anderson and Hernandez. The Mexican was right on the border of offside, but the decision went his way and Rooney tapped in from his square pass.
8.58pmAfter that, United had two more big chances inside a minute just before the half-hour mark. First Nani beat Jaaskelainen with a snap-shot but Potts was alert to clear it just before the line. Immediately after that Smalling rose from a cross but directed his header straight at the Hammers goalkeeper.
8.59pmUPDATE: Still 0-0 at the Emirates but Arsenal are dominating the second half. Twenty minutes left in that one.
9.05pmWest Ham haven't been outplayed by any means, but they haven't really been a threat. They'll need to get into it more to have a chance, and Allardyce could go to his bench fairly early in the second half.
9.06pmJust about ready for the second half to start. I'm surprised at the lack of chances, to be honest, but expect the game to open up as West Ham must come forward more.
45 minHere we go, we're back underway. West Ham defend an early run from Nani down the left.
46 minReally poor touch from Diame there on the right. He had space and West Ham were flooding into the box. At the other end United look to work the exact same goal with Rooney and Hernandez's roles reversed, but Rooney is offside. Correct call.
47 minTop, top defending from Jones as he beats Diame to a Vaz Te through ball before outpacing and outpacing him to clear.
48 minCHANCE! Oh dear Diame, OH DEAR Hernandez! Poor all round as Diame slices a clearance about five feet in the air to Hernandez, who nipped in. He has the whole goal to aim at but curls it over from inside the box. Shocking all round.
49 minAt half-time Roy Keane had his say on the Pep Guardiola to Bayern Munich situation. He thinks he's biding his time for a few years until Ferguson retires. Probably a fair assumption.
50 minWest Ham win a corner after Giggs tackles Diame who was again looking to get in down the right.
50 minLindegaard, under pressure, gets nothing on the cross but United manage to clear.
51 minLots of pressure from West Ham here. Taylor's shot is well blocked but he could have gone down just before from a wild Valencia challenge.
52 minUPDATE! Arsenal 1-0 Swansea (Jack Wilshere) - Arsenal's dominance finally pays off as they get the breakthrough five minutes from time!
53 minAtrocious clearance from Smalling, who slices up in the air. It eventually falls to Lindegaard, however.
54 minGood hold-up from Vaz Te, who finds Taylor. Spence does well to work a cross but it's cleared once more. Just not able to work any shots, West Ham, although they have a free-kick in Matt Taylor range following a Valencia foul.
55 minIt's O'Neil, in fact, who clips towards Winston Reid, but the defender is offside from the ball in.
56 minSlice of luck for Vaz Te there, who chased a lost cause from Spence, before it stayed in off the corner flag and they win a corner.
57 minThe visitors continuing to dominate this half and are winning everything in midfield - Taylor in particular is putting himself about.
58 minUnited finally break forward and Valencia has a chance to cross, but it comes to nothing.
60 minUPDATE: Full-time: Arsenal 1-0 Swansea. The Gunners will travel to Brighton on the 26th.
61 minCHANCE! Taylor finds acres of space in the middle but he cannot find Cole with a cutback. He really should have and the Hammers should be level!
62 minNow United are coming into it a bit more. Valencia again gets free down the right but his cross is cleared for a corner.
63 minCHANCE! A cross is eventually worked to Taylor inside the box, but his effort on his weaker right foot is over the bar. Kevin Nolan is on, as is Jack COllison. Cole is off and I think too Diame.
66 minSAVE! Great work from Jaaskelainen. Hernandez is found after Rafael robbed Potts, but the stopper makes himself big and keeps out the Mexican's left-footed effort. Meanwhile, Anderson comes off for Michael Carrick.
68 minVaz Te has gone up top following the West Ham subs, with Nolan in behind. Cole was doing a good job second half, but what can this combination offer?
69 minUnited have a free-kick here wide on the left, but nothing happens from it.
71 minThis one has hit a bit of a lull. Both sides passing well in the defence, but are being forced back with pressure from the midfield. The hosts are probably just shading it currently.
73 minCHANCE! Nolan wants too much time after being found by Vaz Te. He went to cut inside Smalling but took too many touches and the defender did really well. United work a corner at the other end.
79 minIncredibly harsh penalty call if you ask me. Giggs skips through a couple of challenges and clips into the box where it hits Spence's arm on the run. However justice is done as Rooney blazes it over! Awful penalty!
80 minUnited should have this wrapped up, but as it stands they're still in with a shout. I don't think you can give that penalty, you can't run with your arms by your side!
81 minPoor defensive header from Rafael goes up in the air, but he recovers well to get it away from Taylor and out for a throw.
83 minNo side on top now and there are few chances being created.
84 minGiggs still working really hard here. He finds Rooney whose attempted cross is blocked by Diarra and cleared.
86 minDISALLOWED GOAL! Oh my word an utterly fantastic through ball by Giggs, but Hernandez was lazy and offside. I don't think he was expecting to be found then.
87 minUnited break from a free-kick, with Rooney picking out Hernandez with an angled pass. Giggs too looks for the Mexican but West Ham can clear.
88 minYELLOW CARD! Scholes has only been on a few minutes but he gets his standard booking with a trademark late lunge. Taylor goes down in a heap, awful challenge and a fair booking.
89 minSuperb skill by Giggs in his own half on the left touch line. He wins a free-kick after a set of nifty spins.
90 minThree minutes of time to be added on here. West Ham running out of time.
90+1 minCollison hooks it into the box but without Cole there's not much threat in the air for the Hammers.
90+2 minThere still doesn't seem a lot of urgency from West Ham. They've been better in this half overall but aren't exactly flooding forward now.
9.57pmWell, it wasn't a classic by any means, but it is United who move on to play Fulham next weekend courtesy of Wayne Rooney's early goal.
9.58pmWest Ham improved markedly in the second half, but still were unable to carve out many genuine chances. On balance United deserved it and should have won 2-0 after being gifted a fortuitous penalty which Rooney spurned.
9.59pmThanks for joining me for this coverage and be sure to check out my analysis piece that will go up in about half an hour. Have a great night.