The Blues dominated in the early proceedings with a chance from Gary Cahill, before Marco Alonso fired home after 13 minutes. Chances from Diego Costa, Pedro and Gabriel followed but couldn't add to the scoreline.
Eden Hazard doubled their lead in the 53rd minute, Danny Welbeck and Shkodran Mustafi had good chances but Cesc Fabregas sealed the win. Oliver Giroud got one back in extra-time, but it was too little too late for the Gunners.
Couldn't ask for a better start
With closest rivals Tottenham not playing until the evening, Antonio Conte's side had an excellent chance to extend their lead even further.
There was a slight blip two minutes with Alex Iwobi's effort going inches wide, but Chelsea had the first real opportunity.
Hazard whipped an excellent ball into the area in the 11th minute, Cahill was foolishly unmarked as he heads his effort into the ground but Arsenal are let off as it bounced over the crossbar.
It didn't take long until he home side took the lead, but it was shrouded in some controversy.
Pedro's ball in is met by Costa, but his header comes off the crossbar and into the air. Alonso is there to meet it as it comes back down to earth, it looked a heavy challenge on Hector Bellerin who went off soon after, but the Spaniard's effort stood.
Looking for more
Costa looked to make it two in the 18th minute, as he powered his into the area with his shot from the tight angle nestling the side-netting.
Alonso then looked to turn provider just after the half-hour mark as he pinged the ball into Pedro, it looked easy for Petr Cech but somehow spilled the effort which was luckily cleared by Laurent Koscielny.
Arsene Wenger's side had hardly been in the game, but had their first chance late in the half. A short corner is flicked into the area by Alex Oxlade-Chamberlain, Gabriel was there at the back post and it looked dangerous but Thibaut Courtois managed to punch it away.
Plans out the window
Though he was banned from the touchline Wenger will have had some stern words, but their plans were thrown out early in the second period.
Hazard hadn't scored for three games but returned in some style, he picked it up in his own half leaving Francis Coquelin on the floor. The Belgian managed to make it into the area, leaving Koscielny for dead before firing home.
The Gunners tried to get themselves back in it, and had two good opportunities in quick succession.
A ball in found Welbeck in the 78th minute, it looked to be creeping into the far corner but Courtois was across quickly to palm it away.
Mustafi was there from the successive corner, despite been free at the corner but it was well wide of the mark.
The result seemed pretty nailed on as the game entered the last ten minutes, but it was certified in the 85th minute and it was salt in the wounds for the visitors.
A simple looking throw to Cech turned into a disaster, as he shanked a kick into the sub Fabregas and he made an instant impact as he lobbed the keeper from 30 yards.
The Gunners managed to get one back in extra-time, but it was only a consolation in what another poor performance from the Gunners.
Their man of the match Nacho Monreal was involved once again, as he played an excellent ball into the area and Giroud was there to head low past Courtois despite his efforts.