The influential Eden Hazard set Chelsea on their way when he won and converted a penalty in the first half.
Diego Costa made the game safe with a second goal 12 minutes from time after being set up by former Arsenal captain Cesc Fabregas to maintain Chelsea’s unbeaten start to the season and condemn Arsenal to their first Premier League defeat of the campaign.
After a quiet start Chelsea suffered a scare on ten minutes when goalkeeper Thibaut Courtois suffered a head injury after colliding with Alexis Sanchez, but after lengthy treatment the big Belgian was able to continue.
Things threatened to boil over on 20 minutes when Gary Cahill was fortunate to escape with only a yellow card for a dangerous tackle on Sanchez. The incident sparked an angry confrontation between Arsene Wenger and Jose Mourinho on the sidelines with the Arsenal boss shoving his Chelsea counterpart in the chest and the referee Martin Atkinson was forced to give the pair a ticking off.
Soon after Courtois was forced off to be replaced by Petr Cech as it seemed the goalkeeper had not recovered from that earlier head clash.
Chelsea won a penalty on 27 minutes when Hazard burst past Santi Carzola and Calum Chambers with a lovely jinking run into the box before being brought down by Laurent Koscielny.
Hazard dusted himself down and took the spot-kick and coolly sent Wojciech Szczesny the wrong way before slotting the ball into the net.
Arsenal wasted a great chance to draw level three minutes later when Sanchez picked out Jack Wilshere inside the box, but the midfielder’s first touch was poor, allowing Cech to race off his line to collect the ball.
Chambers had a lucky escape a minute before the break when already on a booking he brought down Andre Schurrle on the edge of the box, but the referee decided to let the young defender off with a warning rather than a second booking and a red card.
Arsenal almost gifted Chelsea a goal just before the hour mark when Hazard beat Chambers down the left and fired over a cross which Mathieu Flamini deflected onto his own post to almost concede an own goal.
Arsenal had claims for a penalty on 64 minutes when Jack Wilshere’s shot from the edge of the box appeared to strike to the hand of Fabregas, but their protests were waved away.
Hazard had a chance to score a second goal 15 minutes from time when Costa superbly held the ball up before finding the winger’s run into the box, but from an acute angle Hazard blazed his shot over the top.
Chelsea did grab the crucial second goal on 78 minutes when Fabregas found Costa’s run with a superb pass over the top and the striker lofted the ball over Szczesny for his ninth goal of the season.