Goals from Didier Drogba and a thunderbolt from Alex put paid to Arsenal as the champions won a titanic match at Stamford Bridge 2-0.
Arsenal passed the ball beautifully but the west Londoners scored the vital goals.
Arsenal was the better footballing sides but tactically Chelsea had, for once got it right.
The visitors had the best of the first half – within the first two minutes they could have scored twice and midway through the half Andrey Arshavin forced a fine save from Petr Cech.
Drogba produced Chelsea's first effort on target of the half with a pile driver of a shot which was well saved by Lukasz Fabianski.
But the home side gradually got a grip on the game and it was Drogba who opened the scoring with a deft back-heeler at the near post after Ashley Cole produced a fine byline cross on 39 minutes.
Arsenal felt they should have had a foul from Ramires at the start of the move but the ref, Mike Dean disagreed and played on.
Once again, Arsenal started brightly in the second half putting Chelsea on the back foot from the off.
But it was Nicolas Anelka who fluffed the easiest chance of his game and probably his career.
Dispossessing Sebastien Squillaci, the Frenchman rounded Fabianski and with the goal gaping embarrassingly ended up putting the ball into the side netting.
Ashley Cole then had a goal disallowed for an offside and Anelka forced Fabianski into a save as Chelsea regained the ascendency.
Marouane Chamakh missed Arsenal’s best chance to get level when he headed past Cech’s post.
It was a decisive miss as Chelsea, with five minutes remaining, scored their second goal which killed off the visitors - and what a beauty it was.
Anelka was fouled 25 yards out and up stepped Alex who produced a blistering trademark right-footed free-kick which arrowed through the wall and smacked the top right hand corner of Fabianski’s net, leaving the goalkeeper floundering.
Chelsea are now four points clear at the top of the league behind Manchester City.
Arsenal are seven points behind the champions.
Chelsea (4-3-3): Cech; Ivanovic (Ferreira 72), Alex, Terry (c), Cole; Essien, Mikel (Sturridge 88), Ramires (Zhirkov 82); Anelka, Drogba, Malouda.
Unused subs Turnbull, Van Aanholt, McEachran, Kakuta.
Scorers Drogba 39, Alex 85.
Booked Ferreira 79.
Arsenal (4-4-1-1): Fabianski; Sagna, Squillaci (c), Koscielny, Clichy; Wilshere (Emmanuel-Thomas 80), Song, Diaby (Rosicky 69), Arshavin (Vela 87); Nasri; Chamakh.
Unused subs Szczesny, Djourou, Denilson, Eboue.
Booked Koscielny 84.
Referee Mike Dean
Crowd 41,828.
Shots on Chelsea 6 Arsenal 5
Corners Chelsea 9 Arsenal 10
Fouls Chelsea 7 Arsenal 13
Offsides Chelsea 7 Arsenal 2