Fabregas scored a goal in each half as the Arsenal crowd enjoyed another dazzling display by their Spanish captain who has now scored three goals in this season's competition.
French midfielders Samir Nasri and Abou Diaby also cashed in against a Dutch side who were outclassed all over the pitch in the Group H clash.
Substitute Jeremain Lens did give a large but rather subdued visiting contingent some late cheer with a consolation goal but Alkmaar, who have started the season poorly, look resigned for a scrap for third spot even though progress is still possible.
With two matches remaining Arsenal top Group H with 10 points from four games, followed by Greek side Olympiakos on six and Standard Liege, who Arsenal host next, on four. Alkmaar have two points.
"It was a brilliant performance because we dominated them technically and tactically," Arsenal manager Arsene Wenger told reporters. "We played with a lot of confidence and overall I'm very happy.
"The competition will get harder but I believe this team has quality and it is down to us to grow and be consistent and then we'll see how far we can go."
Alkmaar coach Ronald Koeman had never lost to Arsenal as coach, first with Ajax and then with PSV Eindhoven and two years ago his PSV side knocked the Gunners out of the competition.
The former Dutch international's record came to a sorry end at the Emirates where the outcome was never in doubt once Fabregas had put the home side ahead after 26 minutes - turning sharply to beat keeper Sergio Romero at his near post.
"I thought our keeper could have done better with their first goal," Koeman said.
"The second goal just before halftime was a very bad moment for us but you have to accept they have such a lot of quality and play so fast we weren't good enough to counter-attack."
Nasri, who played his first match of the season last week in the League Cup after returning from a broken leg, killed the game a minute before halftime when he controlled an Andrei Arshavin pass before slotting a precise shot inside the post.
Russian Arshavin was the provider again seven minutes after the break when his pass found Fabregas who lifted a shot high into the net.
Diaby got in on the act after 72 minutes with a cool finish, again from Arshavin's clever pass.
Alkmaar's Graziano Pelle forced one great save from Manuel Almunia when the game was already up for the visitors before Lens showed great pace by surprising the Spanish keeper with a low shot.
