Goals from Alex Song, Cesc Fabregas and Theo Walcott in a nine-minute spell either side of halftime condemned Carlo Ancelotti's team to another defeat and they have now managed just six points from the last 24 on offer.
Branislav Ivanovic replied for the visitors but the damage was already done as Arsenal ended a run of five consecutive defeats against their London rivals to reclaim second place in the table above Manchester City on goal difference.
"We have matured, I have said that many times. Let's hope it strengthens our belief for the championship and our belief that we are on the right track," said Arsenal manager Arsene Wenger.
"Today we were disciplined, mature and we played for each other. There's still some room for improvement and I'm confident the team will continue to train hard and focus well together."
Arsenal have moved to 35 points from 18 games with unbeaten leaders Manchester United on 37 having played a game less. Chelsea, who started the season in scintillating form but have forgotten how to win, remain in fourth place on 31.
"The table is not good but this is the reality," Chelsea manager Carlo Ancelotti told Sky Sports. "We have to play better and wake up. I am not worried. I have to work and you will have to ask the owner (Roman Abramovich about my future)."
After an unofficial two-week "winter break" caused by the freezing weather conditions in Britain, both sides knew a win was needed to stay in touch with Manchester United.
Chelsea had been impressive in the second half of their 1-1 draw at in-form Tottenham Hotspur 15 days ago and, with Frank Lampard in the starting lineup for the first time since August, there was optimism among the visiting fans that their season could be reignited at a ground that has been kind to them.
However, after 40 minutes of cut and thrust had failed to separate the teams, Chelsea fell apart alarmingly, leaving Ancelotti ashen-face in the technical area where he had stood in a black raincoat for virtually the entire 90 minutes.
If anything Chelsea had looked the more threatening early on with Didier Drogba, scorer of 13 goals in 13 appearances against Arsenal since joining Chelsea, rampaging forward to fire narrowly wide of Lukasz Fabianski's post.
Arsenal's home form has been an irritant this season with three defeats already at The Emirates and there were anxious grumblings around the stadium as their pretty possession football offered little goal threat.
In the end it took some direct action from midfield enforcer Song to lift the psychological shackles Arsenal manager Arsene Wenger feared had begun to grip his side against Chelsea.
A minute before halftime the Cameroonian barrel led forward, played a one-two with Jack Wilshere and, as the ball bobbled back into his path, tucked a low show past Petr Cech.
Six minutes after the break Chelsea imploded.
Michael Essien's attempt to win the ball in midfield inadvertently sent Walcott racing through on goal and the England winger calmly squared it to Fabregas to make it 2-0.
Three minutes later Chelsea were again engineers of their own downfall with Florent Malouda losing the ball under pressure near the center circle.
This time the roles were reversed as Fabregas released Walcott with a perfectly weighted pass and the England winger picked his spot and fired past Cech.
Chelsea's players threw bemused glances towards Ancelotti who immediately substituted the disappointing Malouda.
Ivanovic guided a header past Fabianski after 57 minutes to restore a little hope but as the visitors pushed forward to try and salvage something from a hopeless situation Arsenal wasted several chances to increase their pain on the counter-attack.
Defeat means Chelsea are 10 points worse off than at this stage last season with their title chances disappearing fast.