Arsenal had Gabriel sent off at the end a fiery but goalless first half at Stamford Bridge.
An action-packed end to a 45 minutes lacking chances saw Diego Costa and Gabriel both booked, with the Gunners defender then shown a straight red card for kicking out at the Chelsea striker.
Before then Chelsea were unable to find a breakthrough in an even first half.
The Blues struggled to create clear opportunities, but looked lively in attack with Costa a threat in behind the Arsenal defence, and Pedro and Oscar both prominent.
Pedro shot wide after a neat move, Cesc Fabregas had a long-range strike easily saved by Petr Cech and Eden Hazard claimed for a penalty after going down in the box following a challenge from Garbriel.
But Arsenal also posed problems to a defence without the dropped John Terry.
Chelsea boss Jose Mourinho left Terry on the bench, preferring Kurt Zouma in defence alongside Gary Cahill with Branislav Ivanovic as captain.
And in the main they dealt well with the pace of Theo Walcott despite some threatening moments on the break.
Subs: Blackman, Terry, Mikel, Ramires, Loftus-Cheek, Falcao, Remy.