Togolese striker Emmanuel Adebayor fired the Gunners in front after 10 minutes when he latched onto a Cesc Fabregas defense-splitting pass to slot home with aplomb.
Just one minute later, Spain midfielder Fabregas provided another deft pass to Theo Walcott, who rounded the keeper and tapped into an empty net.
The hosts pulled one back in the 19th minute when Arsenal defender Mikael Silvestre poked Daniel Guiza's volley into his own net.
French midfielder Abou Diaby restored Arsenal's two-goal cushion two minutes later when he muscled his way into Fenerbahce's area before firing a low shot into the net.
Alex Song added a fourth four minutes after the break via a close-range volley.
Spain striker Guiza narrowed the gap in the 78th minute after lobbing the advancing Manuel Almunia.
However, substitute Aaron Ramsey put the result beyond doubt in stoppage time with a powerful low shot from the edge of the area.
Arsenal lead the group with seven points, two ahead of second-placed Dinamo Kiev who, who defeated Porto 1-0.
Porto are third on three points while Fenerbahce lie at the bottom with just one point.