The Gunners had goals from striker Emmanuel Adebayor in the 10th, winger Theo Walcott in the 11th, midfielder Abou Diaby in the 22nd, defender Alexander Song in the 49th and substitute Aaron Ramsey in injury time at Sukru Saracoglu stadium.
Arsenal leads Group G with seven points. Dynamo Kiev, which defeated FC Porto 1-0 on Tuesday, is second with five points. Porto has three points and Fenerbahce has one.
Adebayor, who has been nominated for the Golden Ball award, found the net after penetrating the defense and sliding a low shot past the goalkeeper and inside the post. Less than a minute later, Walcott scored a similar goal before the defense could reorganize.
Samir Nasri squandered a chance to score for the Gunners when the ball was deflected in the 14th minute.
Arsenal defender Mikael Silvestre scored an own-goal in the 19th minute to make it 2-1, but Diaby re-established the two-goal lead three minutes later.
Despite the support of a partisan crowd, Fenerbahce continued its poor domestic form, although Arsenal goalkeeper Manuel Almunia made some spectacular saves in the first half.
Song made it 4-1 four minutes after the break, but Daniel Guiza gave the home fans some hope when he broke free and chipped over Almunia in the 78th.
However, Ramsey scored in the fourth minute of injury time to give the 17-year-old midfielder his first Champions League goal.
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