The Belgian side was rarely troubled in Denmark and goals from Mamadou Oulare and Lior Rafaelov and a Kenneth Emil Petersen own goal gave it a comfortable cushions ahead of the return fixture.
Nicklas Helenius scored a penalty to at least keep AaB interested but it will require a stunning turnaround for it to go through.
Club Brugge flew out of the traps and had two fine chances inside the space of 20 seconds, with Felipe Gedoz seeing both of them.
His first effort, from the edge of the box, was saved by Nicolai Larsen and then he slammed the rebound, from closer range, against the post.
Andreas Bruhn had a header at the other end well blocked and then Anders K Jacobsen had a shot well saved by Ryan as the play went from end to end.
The game really exploded after that, though, as Brugge rattled in two quickfire goals.
Twenty-five minutes in Boli Bolingoli whipped in a cross that Oulare got above Larsen to nod in, and five minutes later the scorer turned provider as his cross was cracked in by Rafaelov, who took aim from just outside the box.
Gedoz took aim in pursuit of a third but was denied, while Oscar Duarte also went close before the half-time break.
The flow of play continued towards AaB's goal after the break as Oulare was stopped by Larsen, but the keeper was helpless on the hour as Petersen sliced a Thomas Meunier cross into his own goal.
AaB was given slight hope when it was awarded a 72nd-minute penalty, with Helenius putting it away after Meunier had brought down Jacob Blabjerg.
It could not mount more of a fightback, though, and Brugge maintained a healthy cushion.
Wolfsburg will take a 2-0 lead to Lisbon next week after the Bundesliga high-flyer claimed a comfortable victory over Sporting in the first-leg of their Europa League last-32 clash.
Bas Dost scored twice in the second-half for the Wolves who were never seriously threatened by a Sporting side which failed net a vital away-goal.
While Dost may claim the headlines, Kevin De Bruyne was the star of the show for Dieter Hecking's men, setting up the Dutchman's second and proving a constant menace to the Sporting defence.
Substitute Carlos Gurpegui scored a 73rd-minute equaliser to earn Athletic Bilbao a 2-2 draw at Torino.
The Italian side trailed 1-0 after Inaki Williams put the Spanish outfit ahead in the ninth minute, but two goals from Maxi Lopez gave the home side a 2-1 half-time lead.
Gurpegui, who entered the pitch in the 58th minute, pulled his team level and almost made it 3-2 but his powerful header hit the crossbar with eight minutes remaining.
Two goals in the space of six minutes put Dnipro in control of its Europa League last-32 against Olympiacos with a 2-0 win in the first leg.
Jaba Kankava opened the scoring five minutes into the second half and just five minutes later Ruslan Rotan's free-kick doubled the host's advantage.
Olympiacos struggled to create clear chances and left Ukraine without an away goal and with an uphill task facing it in the second leg.
