Wayne Rooney and Ji-Sung Park scored as Manchester United won their ninth successive Premiership match.
Rooney's strike was unstoppable
Rooney controlled Mikael Silvestre's brilliant cross before shooting past Jens Lehmann and later crossed for Park to score from close range.
Lehmann had superbly saved from Rooney twice before his goal, while Kolo Toure appeared to divert a strike from the forward on to the post with his hand.
United keeper Edwin van der Sar made good saves from Robin van Persie.
The result means Sir Alex Ferguson's team move back to within seven points of Chelsea, who defeated West Ham 4-1 earlier on Sunday.
United have five games left to catch the reigning champions, including a match at Stamford Bridge against Jose Mourinho's team.
But the victory over Arsenal means United are assured of finishing in the top four - and thus qualifying for next seaon's Champions League.
For Arsenal, though, their ninth away defeat in the Premiership this season leaves them five points behind north London rivals Tottenham in the race for fourth place.
It could have been different for Arsene Wenger's team if they had converted one of their early chances - in a match played in front of a Premiership record crowd of 70,908.
Despite relegating Thierry Henry to the bench Arsenal made the early running. Gary Neville made a superb challenge to deny Emmanuel Adebayor after he had been played through by Alexander Hleb and Van der Sar saved from Van Persie.
It took United a while to settle but eventually they started to threaten, Lehmann punching clear a Cristiano Ronaldo free-kick and then making two superb saves to deny Rooney.
Each time Rooney shot across Lehmann, the first from 20 yards and the second considerably closer but from a tighter angle.
Arsenal looked to break quickly and Van der Sar made a superb save low to his left to thwart Van Persie.
Van Nistelrooy, starting ahead of Louis Saha, started to assert his influence on the contest, shooting wide from a tight angle and forcing Lehmann into action with a header.
And it was a superb through ball from Van Nistelrooy that led to the major incident of the first half.
He played Rooney through and his team-mate took the ball around Lehmann before shooting goalwards.
Toure, struggling to regain his feet, appeared to handle as he dived to his right to try to stop Rooney's strike. The ball was deflected against the post but the incident went unnoticed by referee Graham Poll.
Rooney was not to be denied after the break - the 20-year-old smashing the ball past Lehmann after taking one touch to control Silvestre's cross.
Arsenal went in search of an equaliser, with Adebayor shooting narrowly over and Van Persie failing to convert Emmanuel Eboue's cross.
Eboue brilliantly eluded Rooney before cutting inside but his ball to Van Persie was struck firmly, making it difficult for his team-mate to make a decisive contact.
Arsenal introduced Henry with 18 minutes left but Park's goal took the match beyond the away team.
Man Utd: Van der Sar, Neville, Ferdinand, Vidic, Silvestre, Ronaldo, O'Shea, Giggs, Park (Evra 84), Rooney, van Nistelrooy (Saha 62).
Subs Not Used: Howard, Brown, Pique.
Booked: Vidic, O'Shea, Silvestre.
Goals: Rooney 54, Park 78.
Arsenal: Lehmann, Eboue, Senderos, Toure, Flamini, Hleb (Ljungberg 74), Fabregas (Diaby 69), Silva, Pires, Van Persie (Henry 69), Adebayor.
Subs Not Used: Poom, Djourou.
Ref: G Poll (Hertfordshire).