Eden Hazard opened the scoring for Chelsea in the 27th minute, coolly slotting home a penalty past Arsenal keeper, Wojciech Szczesny.
The Belgium international earned the penalty himself, darting his way into the Arsenal area, only to be brought down by defender Laurent Koscielny.
Diego Costa continued his rich vein of scoring, making sure of three points for the home side when he chipped the ball over Szczesny after latching onto an exquisite Cesc Fabregas pass.
Arsenal manager, Arsene Wenger has now faced rival manager Jose Mourinho 12 times in the Premier League, but has yet to beat him.
In the early kick off of the day, Lious van Gaal’s side picked up an important three points at Old Trafford on Sunday as Everton lost 2-1 to the Red Devils.
The match centred on Radamel’s Falcao’s first goal for United, while at the other end David De Dea earned the plaudits for a first half penalty save against Leighton Baines.