Joris van Overeeem set the Kaaskoppen on their way early on, before Yasmin Ayoub put through his own net just after the half-hour mark.
Frontman Wout Weghorst added a third after the break, heading home a free-kick to put John van den Brom's side firmly in control.
Barring an unlikely turnaround at Utrecht's Stadion Galgenwaard on Sunday, AZ will join fellow Dutch sides PSV Eindhoven and Vitesse in Europe's secondary club competition, albeit at an earlier stage.