Theo Walcott was the hero for Arsenal as his double eradicated a howler of an error from Wojciech Szczesny.
A terrible mistake by Arsenal goalkeeper Szczesny just after half-time presented Carlton Cole with the chance to secure his fourth goal in Boxing Day fixtures after he failed to hold onto a shot from Kevin Nolan.
West Ham could easily have pulled away from Arsenal but the Gunners kept plugging away and got back into the game after Adrian fumbled the ball into the back of the net after Theo Walcott had cut inside and unleashed a shot in the 68th minute.
Walcott then put the Gunners in front with a sublime header after a great piece of work from Lukas Podolski just a couple of minutes after the equaliser.
Podolski then grabbed himself a goal to seal the points after a piece of great work from Olivier Giroud who held the ball up, laid it off to the German who smacked the ball in with the outside of his left foot.
West Ham toiled to get back into the game late on but Arsenal grew in confidence as each goal flew in.