The main talking point in the second half surrounded Rooney, who was dismissed for kicking out at Stewart Downing, but despite having an extra player for over 30 minutes, the away side couldn't score an equalising goal.
Here, Sports Mole has looked back over the contest to determine if the result was a fair one.
On target: 3
On target: 4
Was the result fair?
When West Ham reflect on how much they dominated the second half in terms of ball retention, they will probably feel that their efforts were deserving of a share of the spoils. Yet, David de Gea in the United goal was rarely called into action, while the United defence, which has been extremely shaky of late, held firm. You always felt that with 11 players on the pitch, United would have scored more and taking all of that into consideration, a slender win for Louis van Gaal's men is just about fair.
Man United's performance
With 30 minutes on the clock, United were in cruise control. Rooney was looking sharp as he dovetailed well with the likes of Rafael da Silva, Angel di Maria, Radamel Falcao and Van Persie. There was a point during the first half where they looked like they might score every time that they ventured forward.
Of course, the red card turned the tide, but to be fair to the United defence, they limited West Ham to few chances. Van Gaal is bound to be pleased that his side showed plenty of character by digging in to claim all three points, but he will want some improvement when it comes to keeping hold of the ball. During the second half, they were extremely wasteful and consistently gifted possession back to the Hammers. When a team is a man light, keeping hold of the ball is an absolute must.
West Ham's performance
Up against a nervy rearguard that had two players making their debuts, West Ham posed nowhere near enough of a threat during the first half. When they did, they scored, but aside from that youngster Paddy McNair was allowed to settle in at the back for United, rather than being tested.
They certainly cannot be accused of having not pushed hard for an equaliser, but you would have to say that there wasn't enough quality in the final third. Sam Allardyce will be bitterly disappointed that his side did not take their chance against a vulnerable United.
Sports Mole's man of the match
Paddy McNair: The youngster looked composed throughout and was confident enough to take the ball. When his side came under pressure after Rooney's red card, he defended well, including one clearance when facing his own goal that saved a certain equaliser as Enner Valencia lurked at the back post.
United goalkeeper De Gea, who was at fault for the West Ham goal, has been spared this award by his captain. Rooney had to accept that Downing was just too quick for him, but instead he hacked out at the West Ham midfielder and caught him high up on the thigh. It was wild and he can have no complaints about the red card, which is likely to see him banned for three matches. To make matters worse, Downing was well inside his own half and there was no real danger. It left his side up against it, despite the fact that they held out.
Fair play to Lee Mason because some referees may have bottled the decision to send off Rooney and instead brandished a yellow card. Aside from that, he kept good control of the encounter, which at times threatened to boil over.
Man United: The Red Devils will stay put next Sunday with the visit of Roberto Martinez's Everton to Old Trafford.
West Ham: On the same day, it's a London derby for West Ham, with their former manager Harry Redknapp due to take his Queens Park Rangers side to Upton Park.