Diego Costa’s first-half strike earned Chelsea victory and a league double over title-chasers Arsenal who had Per Mertesacker sent off in the first half.
Arsenal were reduced to 10 men in the 18th minute when the German brought down Costa, who was through on goal.
Five minutes later the Spain striker put the Blues ahead when he tucked home Branislav Ivanovic’s low cross.
Costa also forced a good save from Petr Cech, and Ivanovic’s header was cleared off the line by Nacho Monreal.
The home’s side’s best chance fell to Mathieu Flamini who fired over from close range when he attempted to convert Aaron Ramsey’s through-ball with a kung-fu kick.
Victory sees the Blues move up to 28 points and 13th position – their highest placing since 26 October. Defeat for the Gunners leaves them in third, three points behind Leicester who have 47 points.