Chamakh celebrates scoring the third goal
Andrey Arshavin scored one and set up Samir Nasri as Arsenal led 2-0 at half time.
But Ciaran Clark volleyed Villa back into the game in the 52nd and then headed in another after Marouane Chamakh scored a third for Arsenal.
Arsenal made sure of the victory in stoppage time when Jack Wilshere scored his first league goal for the north London club.
The Gunners had thrown away a 2-0 lead against Tottenham last Saturday before losing 3-2 and were beaten by Braga in the Champions League on Tuesday.
Villa has collected one point from its last three league matches.
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