Cheikhou Kouyaté and Mauro Zárate scored for the Hammers with Arsenal keeper Petr Cech at error on both goals.
World Cup winner Mesut Özil was given a starting spot by Arsenal boss Arsene Wenger while summer signing Cech made his league debut for the Gunners.
Jack Wilshere, Flamini and Rosicky and striker Danny Welbeck were all out injured while Alexis Sanchez has missed the game after being given extended leave after the Copa America.
Arsenal have a tough away trip to Crystal Palace next weekend.
Stadium: Emirates Stadium
Kick-Off: 15:00 GMT
Cech; Debucht, Mertesacker, Koscielny, Monreal; Coquelin, Cazorla, Ramsey; Ozil, Oxlade-Chamberlain, Giroud
West Ham lineup:
Adrian, Tomkins, Reid, Ogbonna, Cresswell, Oxford, Noble, Kouyate, Payet, Zarate, Sakho