The hosts made five changes for the game with Chris Smalling, Michael Carrick, Anderson, Tom Cleverley and Chicharito all coming in. West Ham, meanwhile, also opted to freshen up their team with Guy Demel, James Collins, Matt Jarvis and Matt Taylor all starting.
Having gone behind nine times already this season, Manchester United this time started the game strongly and took the lead with just 33 seconds on the clock, the fastest Premier League goal so far in 2012-13.
A measured pass from Carrick found Van Persie just inside the West Ham box. The Dutchman's exquisite turn and first touch took him past Winston Reid and his second was a finish which deflected off James Collins and looped over a stranded Jussi Jaaskelainen to hand United the lead.
The early goal shocked West Ham but they slowly came back into the game, with their high balls into the box causing the hosts problems at the back.
Indeed with just 10 minutes on the clock, a left-wing free kick found Nolan in space at the near post. The former Newcastle man flicked a header goalwards, that looked to have Lindegaard beaten, but only flew into the side netting.
Midway through the first half, Andy Carroll came close to an equaliser when a weak clearing header from Jonny Evans fell kindly for the striker but his turn and volley from close range flew over the bar.
In contrast, the hosts were finding chances hard to come by, although Anderson and Chicharito both forced Jaaskelainen to save well on the half-hour mark with low, curling efforts.
The second half saw West Ham start strongly yet United enjoyed the most chances after the break. A Cleverley volley after Van Persie's touch forced Jaaskelainen to tip the ball over the bar before the goalkeeper was called into action again, this time saving comfortably from the Dutchman's free kick.
And the Finn was called into action again on the hour mark after Anderson picked out an unmarked Rooney lurking on the edge of the box. The England man attempted to curl a shot into the far corner but again the West Ham keeper was equal to it, tipping his effort around the post.
Perhaps the best chance of the game fell to the visitors with just eight minutes to go, however. Yet another long ball into the box from Collins was brought down by substitute Carlton Cole, who fired goalwards on the turn but could not beat Lindegaard, who saved crucially for the hosts.
As the 90-minute mark approached and just the one-goal lead remained, a degree of anxiety crept into the hosts' game, but they managed to hold on to preserve their lead and their position at the top of the table.