Goals from Marcos Alonso, Eden Hazard and Cesc Fabregas put the runaway league leaders in complete control of the contest before a late Olivier Giroud header provided scant consolation for the visitors.
Arsenal have now lost on their last five visits to Stamford Bridge, but the away side almost broke the deadlock inside two minutes when a defensive mix-up between Thibaut Courtois and David Luiz presented Alex Iwobi with a chance, only for the winger to feed his shot narrowly past the far post.
Chelsea soon began to gain a degree of control over the match and created their first chance in the 11th minute when Gary Cahill rose highest in the area to meet a free kick, only to plant his header into the ground and see it bounce harmlessly into the arms of Petr Cech.
The hosts did open the scoring just two minutes later, though, as Alonso towered over Hector Bellerin to nod a rebound in after Diego Costa had seen a header of his own crash against the crossbar seconds before.
Bellerin suffered a heavy blow in competing for the ball with Alonso, and the Spaniard - who was rested for the midweek defeat to Watford - was forced off as a result of the injury, being replaced by Gabriel Paulista.
Chelsea continued to look the most likely to get the game's second goal as the half wore on, with Costa slamming one shot into the side-netting before Cech spilled a tame Pedro strike behind for a corner.
Arsenal began to come into the match towards the end of the first half, though, and created their first big chance with seven minutes remaining when Gabriel was left unmarked inside the area but could only plant his header straight at Courtois.
The Gunners came close again in first-half stoppage time when they worked the ball to Mesut Ozil, who cut inside but fired his low effort too close to the keeper.
Arsene Wenger's side were unable to level things up before the interval, though, and within eight minutes of the restart they saw the game slip beyond their reach courtesy of a stunning solo effort from Hazard, who collected the ball in his own half and shrugged off the challenge of Francis Coquelin before advancing into the box, beating Laurent Koscielny and firing his finish past Cech.
Hazard's magic all but ended Arsenal's chances in the match - and arguably in the title race too - and it took the visitors until the 78th minute to come close to a response when Danny Welbeck saw a header clawed away by Courtois before Shkodran Mustafi planted a header wide of the near post from the resulting corner.
Any slim hopes the visitors may have had of hauling themselves back into the match evaporated with five minutes remaining when Cech gifted Chelsea a third goal, giving the ball straight to Cesc Fabregas, who lifted it over the keeper to cap off the home side's scoring against his former club just a minute after coming on.
The hosts were not content with just three goals, though, and went pushing for a fourth in the closing stages, with Alonso and Costa both failing to make the most of presentable opportunities.
Arsenal did pull a goal back in stoppage time when Courtois was unable to keep Giroud's header out despite getting a hand to the ball, but it was scant consolation for Wenger's side as they saw their title hopes all but ended at the hands of their London rivals.
Chelsea have now won 11 consecutive home matches in all competitions, while Arsenal have lost back-to-back league games for the second time this season - the first time that has happened in a single campaign since 2011-12.