The Gunners moved back into second place in the table after finally beating Chelsea for the first time since November 2008 as the Blues' poor run continued.
Arsenal had lost each of their previous five matches against Chelsea, but Alex Song put them ahead before half-time, with quickfire strikes from captain Cesc Fabregas and Theo Walcott giving Arsene Wenger's side a three-goal cushion.
Chelsea reduced the deficit through Branislav Ivanovic, but there was no way back for Carlo Ancelotti's men, who have now taken just six points from their last eight league games - the club's worst run since 1998.
Arsenal, beaten at Manchester United in their previous game, were positive during the opening exchanges at the Emirates Stadium on Monday night.
Robin van Persie almost collected Song's chip into the box, but the ball bounced just ahead of the Dutch striker.
There was a warning with Chelsea's first meaningful attack as Didier Drogba - with 13 goals in as many games against the Gunners - shrugged off his marker to drag a 20-yard shot wide.
John Terry pulled back Van Persie as the Gunners looked to break on the half-way line, but a stern talking-to from referee Mark Clattenburg was all the Chelsea skipper received.
The home side continued to press, and had a penalty appeal waved away when Florent Malouda looked to have made some contact with Van Persie at the edge of the box.
Nasri's 25-yard free-kick was on target, but held by Petr Cech.
Walcott latched on to a long ball over the Chelsea defence, but just as he aimed to cut back into the area, his touch was poor and Terry recovered to clear.
On 29 minutes, former Gunner Ashley Cole went into the referee's book for tripping Walcott as his England colleague turned him on the right touchline.
Van Persie was then put through into the left by Nasri after some clever one-touch passing, the Dutchman snatched at his angled shot, which flew high and wide.
Salomon Kalou was perhaps fortunate to receive only a yellow card after jumping in, studs up on Gael Clichy.
Arsenal increased the tempo as half-time approached.
Walcott scampered into the right side of the Chelsea penalty area and was blocked by Cech at the near post before the goalkeeper turned over Nasri's chip which was looping into the top-left corner.
The Gunners finally made the breakthrough after 44 minutes.
Jack Wilshere and Song exchanged passes on the edge of the area, with the Cameroon midfielder carrying the ball into the box.
Paulo Ferreira slid in and tripped Fabregas, but Song had the presence of mind not to wait for a whistle and swept a low left-footed shot across goal and into the bottom right corner.
Chelsea made a change at the start of the second half as the creative Brazilian Ramires replaced John Obi Mikel.
Arsenal, though, had a two-goal cushion after 51 minutes.
Van Persie held the ball up 30 yards out, and, as he was closed down, Michael Essien's challenge inadvertently pushed the ball straight to Walcott clean through on goal.
The England winger dashed to the edge of the box, where he drew Cech before sliding the ball along to Fabregas and the Arsenal skipper made no mistake from 15 yards.
Chelsea had little chance to recover, as Walcott smashed in goal number three just 90 seconds later.
Walcott robbed Malouda and fed Fabregas, who repaid the favour by sending the Arsenal winger away down the right for him to slot a low shot into the bottom left corner.
Ancelotti had to do something, and sent on Gael Kakuta, replacing Malouda.
Chelsea snatched a lifeline after 57 minutes when Drogba's free-kick floated through to the six-yard box, where it was nodded in by Ivanovic.
Given Arsenal's recent record of failing to hold on to winning positions, the visitors rallied.
Chelsea made a final change when Ferreira was replaced by Jose Bosingwa.
Arsenal just about weathered the storm as the contest entered the final 20 minutes.
Nasri should then have done better when Kakuta's tame back-pass presented him with the ball 10 yards from goal, but Cech was out quickly to block.
With 18 minutes left, Walcott was replaced by defensive midfielder Abou Diaby who made his first appearance since mid-October, before Marouane Chamakh came on for Van Persie.
Diaby's close-range effort was blocked by Frank Lampard and Kakuta's bundled effort was ruled out for offside as the Gunners closed out for a long-overdue victory against their championship rivals and moved within two points of leaders Manchester United, albeit having played a game more.
Chelsea stay fourth, four points behind their capital rivals.