Two goals from Didier Drogba and an own goal by Thomas Vermaelen were enough to give Carlo Ancelotti's side all three points.
Chelsea reaped the benefits of playing a patient game and allowing the Gunners to come on to them and then soak up whatever Arsene Wenger's players had to offer.
Arsenal had the lion's share of the game but had no real cutting edge and, just like in the loss against Sunderland last week, they sorely missed the injured Robin van Persie.
The game began at a frantic pace and the Gunners showed the greater attacking intent, with Chelsea happy to work on the counter-attack.
With van Persie missing with his ankle injury, Eduardo was given the role of operating as the spearhead of Arsenal's attack, supported by Andrey Arshavin and Samir Nasri just behind.
Chelsea had a golden opportunity in the 18th minute after a delightful ball from Frank Lampard that picked out Nicolas Anelka.
The former Gunner failed to capitalise under pressure from Bacary Sagna and the chance went begging.
Eduardo was just inches away from getting a toe to a ball driven into the box by Arshavin in the 27th minute but Petr Cech gathered well in the end.
Arsenal were caught napping in the 41st minute when Ashley Cole was allowed to run on to a Joe Cole pass on the left side of the area.
The left-back then sent a cross into the area for Drogba to re-direct towards goal, with the ball eventually going in off the bar.
The Gunners went two behind four minutes later when Vermaelen turned another Ashley Cole cross into his own net.
Wenger decided to gamble in the second half by sending on Theo Walcott in place of Alexandre Song.
That gave Arsenal added impetus but a more vulnerable centre. The Gunners put the ball in the net in the 48th minute but Arshavin's effort was chalked off for a foul on Cech.
A further injection of pace in the Arsenal attack came when Eduardo was replaced by Carlos Vela as Wenger tried to keep the attacking momentum going.
Vela had a solid penalty claim waived away by referee Andre Marriner, much to the frustration of the home fans and their manager.
Chelsea just stuck to their gameplan, packed their defence and played on the counter-attack.
They almost added another in the 63rd minute when Manuel Almunia made a superb close-range save from a Drogba cross that deflected off Lampard.
Drogba claimed his second and Chelsea's third in the 86th minute with a delightful 25-yard free-kick that he sent into the top right-hand corner beyond Almunia's reach to kill off any hopes the Gunners had of mounting a late fightback.