Goals from Danny Welbeck, Adnan Januzaj and Ashley Young ensured victory, while Carlton Cole netted a consolation for the visitors.
Here are the player ratings of the United players.
David De Gea – 6/10
Largely untroubled by West Ham, the Spanish stopper showed his authority by claiming a cross in dominant fashion but was left exposed for the Hammers’ goal.
Patrice Evra – 6/10
Another very average performance from the France international, who must realise his place is at risk with January signings in the position likely.
Jonny Evans – 8/10
Commanded the back four in the absence of Nemanja Vidic and showed his boss that he is capable of replacing the old guard in United’s defence.
Chris Smalling – 7/10
Looks a lot more comfortable at centre-half as opposed to right-back and made some telling interceptions and clearances.
Rafael – 7/10
Looked to get forward as often as possible, and combined well with Antonio Valencia to find space down United’s right.
Phil Jones – 7/10
Showed a fair amount of poise on the ball and battled well in the boiler room. A number of commanding runs forward in the first half showed his athleticism.
Tom Cleverley – 6/10
Provides energy and industry in the centre of the park, but his ability on the ball is in question. Seemingly always looks for the easy pass sideways or back.
Adnan Januzaj – 8/10 Man of the Match
Looked like United’s most dangerous attacker, with fantastic technique and trickery on the ball. Took his first United home goal very well, but must be careful of theatrics after being booked for diving.
Antonio Valencia – 7/10
Took up some excellent positions and got a fair amount of joy on the flanks, but his end product still remains a frustration. Picked the wrong option a couple of times, and his shooting was wayward.
Wayne Rooney – 8/10
Commanding in possession as always, Rooney is United’s main creative spark and repeatedly took up positions that West Ham struggled to combat.
Danny Welbeck – 7/10
Looked sharp and took his goal very well before being substituted. Moyes will hope his injury is not too serious.
Javier Hernandez – 7/10
Worked hard after being introduced and was unlucky not to get a goal for his efforts. Had to endure some heavy-handed treatment from the opposition.
Ashley Young – 7/10
Another goal for the England winger, which he rifled into the roof of the net. Put a couple of tantalising crosses in and looks to have regained a degree of confidence.
Alex Buttner – 6/10
Showed more attacking intent in 15 minutes than Evra did in 75. However, played Cole onside for West Ham’s goal.