Samir Nasri got the first goal for the Gunners, after an attacking threat, to grab his fourth and fifth of the season.
Rafael Da Silva, one of the substitutes of United, volleyed Home to give to the Reds a hope, but it was not enough as Arsenal claimed the points.
It was a victory that Arsenal merited, with United creating and wasting chances and never carrying the same sense of self-belief as The Gunners was in highly charged atmosphere.
United: Van der Sar, Neville (R. Da Silva 63), Ferdinand, Vidic, Evra, Ronaldo, Anderson (Giggs 72), Carrick, Park, Rooney (Tevez 77), Berbatov. Subs not used: Kuszczak, Nani, O'Shea, Evans.
Goal: R. Da Silva (90th minute)
Booked: Evra and Carrick.
Referee: Howard Webb.
Man-of-the-Match: Arsenal's Samir Nasri.
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