Arsene Wenger's side had repeatedly failed to produce the goods in crunch matches against their London rivals, but they finally rose to the occasion as goals from Alex Song, Cesc Fabregas and Theo Walcott gave them a vital victory at the Emirates Stadium.
Branislav Ivanovic got one back for Chelsea but the damage had already been done and Blues boss Carlo Ancelotti could face a fight to save his job after his team's sixth league game without a win.
Arsenal's triumph - their first in 12 games against Chelsea and United - lifted them back into second place and within two points of the leaders.
In contrast, Chelsea's title hopes are close to being extinguished. They are six points behind United, who have a game in hand, and even a place in the top four can't be taken for granted on this woeful form.
Although Ancelotti's team had taken just six points from their last seven matches, the club's worst run since 1998, they should have been able to draw inspiration from their dominance over Arsenal in recent years.
Didier Drogba threatened early on when he latched onto Frank Lampard's pass and smashed his shot just wide.
The Gunners looked hamstrung by nerves during a tame 1-0 defeat against United in their last match and Wenger knew they needed a more dynamic performance this time.
Wenger's players rose to the challenge in impressive fashion and controlled possession right from the start.
Samir Nasri brought Chelsea goalkeeper Petr Cech into action for the first time with a long-range free-kick.
Wenger's side kept probing and Robin van Persie blazed over before Cech plunged at Walcott's feet to block the winger's shot.
It took an even better save from Cech to keep Chelsea on level terms when he stretched every sinew to tip over Nasri's deft chip.
Arsenal's pressure finally told in the 44th minute as Song surged into the penalty area after playing a one-two with Jack Wilshere.
The ball broke towards Fabregas and, as the Arsenal captain collided with Paulo Ferreira, Cameroon midfielder Song seized his chance and drove a low shot past Cech.
Lampard's presence in the Chelsea starting line-up for the first time in four months after hernia and groin injuries was supposed to inspire the Blues, but the England midfielder was well off the pace.
If Ancelotti read the riot act at half-time, he must have been sorely disappointed with the response from his lacklustre stars.
In the space of 90 seconds, two sloppy pieces of Chelsea defending presented Arsenal with the goals that put the result beyond doubt.
First, Michael Essien's 51st minute tackle on Fabregas sent the ball into Walcott's path.
Walcott was then granted too much space by former Arsenal defender Ashley Cole and he was able to sprint clear before sliding a pass to Fabregas, who stroked his shot past Cech.
Arsenal were rampant now and, with Chelsea looking more shambolic by the second, Walcott took full advantage as he caught Florent Malouda in possession and flicked a pass to Fabregas.
The Spaniard's return ball put Walcott through on goal and he drove a fine finish into the far corner of Cech's net, prompting a furious response from Drogba, who argued with team-mate John Terry before the restart.
Even when Ivanovic reduced the deficit by heading Drogba's free-kick home in the 57th minute, there was little realistic hope of a Chelsea comeback as Arsenal cruised to their most important win of the season.