Spanish ace Fabregas scored either side of the interval.
On 26 points, he beat keeper Sergio Romero at his near post to open the scoring and seven minutes after the break he latched onto an Andrei Arshavin pass to slot home with aplomb.
Russia ace Arshavin also set up Samir Nasri, who scored on the stroke of halftime with an accurate shot, before releasing Abou Diaby who netted Arsenal's fourth with 18 minutes remaining.
Substitute Jeremain Lens scored a consolation goal for visitors Alkmaar in the 82nd minute.
Meanwhile, Standard Liege beat Olympiakos Piraeus 2-0, thanks to strikes from Dieumerci Mbokani and Milan Jovanovic on 31 and 88 minutes respectively.
Arsenal now on top of Group H with 10 points, four ahead of Olympiakos Piraeus.
Standard Liege are second on four points, while Alkmaar are last with two.