A brace of goals from Samir Nasri was enough, although a last-minute response from Rafael Da Silva set up a tense finish to an enthralling game.
In the light of recent results, it was a must win encounter for the depleted Gunners.
They could have gone behind in the first minute when Mikael Silvestre passed the ball back to his keeper, who gathered momentarily with his hands leading to a free-kick inside the area.
As is often the case with such free-kicks, it was too close to goal and Cristiano Ronaldo's shot cannoned back of an Arsenal defender to Michael Carrick, whose poorly struck shot bobbled through a crowd and wide of the post.
Without the injured Emmanuel Adebayor and the suspended Robin van Persie, the Gunners relied on the lone attacking figure of Nicklas Bendtner.
It was a big responsibility on the 20 year-old's shoulders and he should have done better on 11 minutes when he rose unchallenged to meet Gael Clichy's cross from the left, but his effort flew high over the bar.
It was all Arsenal at this point, with Manchester United pegged back. Abou Diaby had a shot from inside the box blocked on 15 minutes after Edwin van der Sar only half-cleared a Bacary Sagna free-kick.
Wayne Rooney should have scored at the other end on 17 minutes after a good counter-attacking move set up by Dimitar Berbatov, but he lifted his shot high over Manuel Almunia's bar.
The Gunners took the lead on 22 minutes when United conceded another free-kick on the right.
Sagna's delivery was cleared by United but only as far as Nasri, who instantly sent a rocket of a half-volley back towards goal, taking a deflection on its was past van der Sar.
United looked dangerous on the counter-attack after the break, but a combination of a disciplined offside trap and sometimes desperate defending kept Sir Alex Ferguson's side out.
The Gunners got the vital second goal within three minutes of the re-start and again through Nasri.
A threaded pass from Cesc Fabregas picked up the Frenchman's run into the right side of the area for him to dispatch an instant shot across goal and beyond the helpless United keeper.
The visitors should have pulled one back a minute later and Ronaldo thought that he had. A deep cross from the left by Ji-Sung Park found the Portugal winger in acres of space.
He coolly tracked the trajectory of the ball and picked his spot but, to the astonishment of all, it rolled across the oncoming Almunia and wide of the left post.
United did pull a goal back through substitute Rafael in the 90th minute to set up a nervous end to the game.
Arsenal had failed to clear their lines and kept giving possession back to United around then area. The ball eventually fell to Rafael, whose shot beat Lukasz Fabianski, who had come on for the concussed Almunia.
The treatment given to the Arsenal keeper after he received a kick to the head earlier in the game meant that six minutes of injury time were added.
The tension was nail-biting as the Gunners fans and players must have been haunted by the recent submission to Spurs when they gave up a 4-2 lead.
But Arsenal held their nerve and their lead this time to capture all the points and keep themselves in the championship race.