Zwolle, who are still searching for their first win of the season, had no answer after Ali Elkhattabi gave AZ the lead on three minutes.
AZ killed off the game in a ten-minute spell either side of the interval, with Kenneth Perez, Stein Huysegems and Barry van Galen doing the damage.
RBC Roosendaal came from behind to beat RKC Waalwijk 2-1. Goals from Sidney Lammens and Essad Razic cancelled out Said Boutahar's opener for RKC.
Heerenveen suffered a shock 2-1 home defeat to NEC Nijmegen, while Groningen heaped more misery on Vitesse Arnhem.
Heerenveen succumbed to goals either side of half time by Dennis de Nooijer and Youssouf Hersi, with Georgios Samaras' effort late on proving nothing more than a consolation.
Didier Martel gave Vitesse an early lead, but they were undone by two goals in the last five minutes from Arvid Smit and Martin Drent for Groningen.
Rob Penders netted an injury time goal to rescue NAC Breda, after Gijs Cales thought he had given Den Haag victory.
Match summaries
ADO Den Haag v NAC Breda
AZ Alkmaar v Zwolle
Groningen v Vitesse Arnhem
Heerenveen v NEC Nijmegen
