The Gunners suffered an early blow when Mertesacker was sent off for bringing down Diego Costa as the last man.
Arsenal conceded just minutes later when Costa made the most of some questionable defending.
Mesut Ozil’s 100th game for the north London based club ended in a disappointing defeat. Arsenal would have ended the week as league leaders had they beat the Blues.
Arsenal v Chelsea
Stadium: Emirates Stadium
Arsenal: Cech, Bellerin, Koscielny, Mertesacker, Monreal, Flamini, Ramsey, Campbell, Ozil, Walcott, Giroud
Subs: Ospina, Gibbs, Chambers, Gabriel, Elneny, Oxlade-Chamberlain, Alexis
Manager: Arsene Wenger
Chelsea: Courtois; Ivanovic, Zouma, Terry (c), Azpilicueta; Mikel, Matic; Willian, Fabregas, Oscar; Diego Costa
Subs: Begovic, Cahill, Baba Rahman, Loftus-Cheek, Traore, Hazard, Remy.
Manager: Guus Hiddink
Goals: Diego Costa