The Blues were efficient and took every chance that came their way. The Gunners were the complete opposite. They created more, but failed miserably in front of goal, although Kolo Toure found the net in spectacular fashion, unfortunately it was his own.
The other Chelsea goals came from Alex and Nicolas Anelka with Florent Malouda poking home a rebound in the dying minutes. Substitute Nicklas Bendtner scored a consolation.
Arsenal began the game the brightest. Both Samir Nasri and Theo Walcott were causing the Chelsea defence problems. Walcott should have done better on two occasions in the opening ten minutes, but fired one shot straight at Petre Cech and another over the bar.
The best chance fell to Abou Diaby in the 13th minute after Walcott had dragged the ball back to him in the Chelsea box. All that was needed was a cool head and sure foot to place the ball beyond Cech. Diaby had neither and screwed the ball wide of the left post.
Arsenal were wasting too many chances and another went begging in the 19th minute after Diaby found Walcott on the angle of the right side of the area but the England attacker's first time shot flew just wide of the right post with Cech well beaten.
Lukasz Fabianski was called into action for the first time in the 22nd minute when he denied Frank Lampard after Ashley Cole's good run down the left opened up the opportunity for the midfielder.
Alex Song was next to miss a gilt-edged opportunity when he fired wide from point-blank after Chelsea had failed to properly clear Cesc Fabregas' free-kick from the left flank.
Chelsea took the lead against the run of play through Alex in the 28th minute when a free-kick delivered into the box by Didier Drogba was headed home by the Brazilian defender off the inside of the bar.
The free-kick was unnecessarily conceded by Fabregas who earned himself a booking. The result was his team went a goal behind and they were almost reduced to ten men when the Gunners captain lunged into Lampard.
Phil Dowd looked certain to give the Spaniard his marching orders. Instead he received a stern talking to. Arsenal's rhythm was upset and it got worse five minutes before half-time.
Anelka run into space midway in the Arsenal half before unleashing a fierce 30-yard drive that swerved away from the diving Fabianski to finish in the right corner of the net.
It got worse for Arsenal barely three minutes after the restart. Cole got away down the left flank and turned in an innocuous, bobbling ball into the Arsenal area. Inexplicably, Toure slid in and put the ball into his own net past Fabianski.
Arsenal's inefficiency in front of goal continued in the same vein as in the first half. Robin Van Persie made it easy for Cech with a tame shot in front of goal on 50 minutes and then Walcott fired wide of the left post when in on goal on the right side of the area.
Bendtner pulled one back for the Gunners when he climbed above the Chelsea defenders to head home Bacary Sagna's cross from the right.
The Danish striker came close to repeating the feat in the 75th minute but this time his header was well saved by Cech. The Chelsea keeper was then on hand to deny Van Persie in the 80th minute as the Gunners began to add a bit more urgency to their game.
Just as Arsenal seemed to have regained a foothold in the game, Malouda made it 4-1 with a tap-in in front of goal after Fabianski had parried the Frecnhman's first effort, Anelka then hit the post but the rebound fell to the Chelsea winger who slid in to direct the ball into the net.
Any glimmer of a resurgence from the Gunners was killed off along with their 21-game unbeaten run in the Premier League.
The victory allowed Chelsea to wrap up third spot and so avoid the tricky preliminary round in next season's Champions League.