Sir Alex Ferguson's side will now lift the trophy this Wednesday at Stamford Bridge in what was billed as a championship decider with Chelsea.
Jose Mourinho's men gave it their all in the second half despite being a man short and came close to keeping their championship hopes alive.
It was a game that Chelsea had to win, but with the loss of their main striker, Didier Drogba, as well as the absence of Andriy Shevchenko, Salomon Kalou looked a lonely lightweight figure in attack.
Shaun Wright-Phillips looked to be the liveliest of the visiting makeshift attack.
Chelsea's most potent weapon is their heavy artillery in midfield, with Michael Essien and John Obi Mikel restricting the space that Abou Diaby, Cesc Fabregas and Denilson had to work in.
The result was a largely stagnant opening half without any real clear-cut goalscoring opportunities.
A defensive error by Chelsea almost allowed Emmanuel Adebayor in on 25 minutes, but the threat was eventually quashed by John Terry and Khalid Boulahrouz.
At the other end ten minutes later, Joe Cole had a shot across goal after the ball was mis-kicked by Gilberto.
The Gunners could have gone ahead though in the 36th minute when Adebayor was through on the right side of the area, but the Togo international didn't quite connect with the ball and in the end the Chelsea keeper made a comfortable save with his legs.
The half ended in controversial fashion though. Julio Baptista bundled his way into the Chelsea box in the 42nd minute but Boulahrouz shoved him in the back to deny a goalscoring opportunity.
Referee Alan Wiley pointed straight to the spot before showing the Dutchman a red card.
Arsenal captain Gilberto stepped up to fire into the bottom right corner of the net and sent Petr Cech the wrong way for the Gunners to lead 1-0 at the half-time whistle.
The Gunners began brightly after the re-start with Adebayor firing a half-volley across goal and just wide of the right post on 47 minutes.
With Chelsea down to ten men the gaps in midfield began to open up, especially as Michael Essien was now playing at centre-back in place of Boulahrouz.
The Gunners' tactic was to use the width of the pitch to draw the visitors out and former Chelsea defender William Gallas came closest to doubling Arsenal's tally on 65 minutes when he headed Fabregas corner over the bar.
It was Chelsea who claimed the next goal on 70 minutes.
Arsenal had only half-cleared a Frank Lampard corner allowing Wright-Phillips to get a cross into the near post for Essien to connect with a diving header which beat Jens Lehmann.
From then on Chelsea stepped up a gear as Arsenal seemed to sit back.
Essien should have made it 2-1 on 82 minutes but blasted his shot high and over the bar.
Lampard seized on some slack play by Fabregas to test Lehmann from 25 yards, but the German keeper turned the ball around his right post.
Lehmann then made a superb save from Kalou in injury time and the game had suddenly been transformed into a match of end-to-end attacking.
As the clock ticked away and Chelsea pushed forward, Arsenal were hitting the visitors on the counter-attack.
In the dying seconds of injury time, Emmanuel Eboue's shot from the right cannoned off the bar with Cech well beaten.
The referee then blew for the final whistle and Chelsea's valiant attempt to retain the championship came to an end.