Wenger responded to the dismissal by taking off in-form striker Olivier Giroud for Gabriel Paulista, much to the disappointment of the French forward and the Emirates crowd.
Costa found space in between three Arsenal defenders and finished a clinical volley at the near post following a whipped cross from Branislav Ivanovic, who was playing his first game since signing a new contract with the title holders.
Flamini had a great chance to level the scores in first-half injury time after running onto a lobbed pass from Mesut Ozil, but wasted the opportunity by volleying well over the bar.
Chelsea were denied a potential penalty as Cesc Fabregas was barged over in the Gunners’ area by Laurent Koscielny after 59 minutes, and Wenger then brought Alexis Sanchez on to try and turn the game around. ESPN