With Craven Cottage hit by heavy rain, both teams went for eachother early and it was Olivier Giroud who handed the Gunners a 14th minute lead.
The France striker reacted first to a deflected effort from Aaron Ramsey and forced the ball past David Stockdale in the Cottagers goal.
But Lukas Podolski struck five minutes before the break with a rocket after clever wing play from Theo Walcott, so giving the visitors a comfortable 2-0 halftime lead.
After some threatening moments again from Taarabt early in the second-half, Podolski struck his second and Arsenal's third on 67 minutes.
A break from Walcott set up Santi Cazorla, whose pull back was thumped past Stockdale by the German.
Before the goal, Darren Bent came on for his Fulham debut and it was the England striker who pulled a goal back for the hosts on 76 minutes.
A well worked move between Sascha Riether and Dimitar Berbatov saw the Bulgarian's cross-shot spill into the path of Bent for a simple tap in.
However, any thoughts of a comeback were snuffed out by Arsenal, with Wilshere on and controlling the midfield for the remaining quarter of the game.
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