Simon Poulsen put AZ ahead just after the half-hour mark, bundling in from close range after Go Ahead Eagles failed to clear a corner for the visitors.
The home side edged the possession at De Adelaarshorst, but AZ generally controlled proceedings and John van den Brom's men eventually doubled their lead with 58 minutes gone.
Dabney dos Santos played a well-timed throughball into the edge of the area for Robert Muhren and the forward stroked beyond Mickey van der Hart in the hosts' goal, lifting AZ above Feyenoord ahead of their clash with Excelsior on Sunday.
Zwolle suffered their third successive league defeat, losing 3-2 at ADO Den Haag to fall five points behind AZ in the battle for automatic continental qualification.
The visitors had seemingly stolen a point at the death, coming from two down to go level in the first minute of second-half stoppage time thanks to goals from Ben Rienstra and Mustafa Saymak.
But Michiel Kramer netted his 14th league goal of the season a few moments later to secure a dramatic late win for Den Haag.
The day's final game saw Utrecht claim a 1-1 draw at Heracles, with the home side - who had Jeroen Veldmate dismissed late on - failing to hoist themselves out of the bottom three.
