It was announced on Thursday that the Netherlands legend would miss the game through ill health, but his charges were in fine form on Saturday.
Guus Hupperts put the visitors ahead with just six minutes on the clock and Muamer Tankovic doubled their advantage before the break.
The deficit was reduced by Mart Lieder in the 53rd minute as Dordrecht, promoted from the second tier last season, threatened to make a game of it.
But Tankovic turned provider to set up Steven Berghuis for his third of the campaign five minutes later as AZ secured their first triumph since the opening day.
Heracles' miserable start to the season continued as they surrendered an early lead to lose 3-1 at Excelsior.
Forward Denni Avdic got the rock-bottom visitors up and running just 10 minutes in, but Jeff Stans wiped out that advantage in the first half before scoring a penalty early in the second.
Former Heracles man Daryl van Mieghem rubbed salt in the wounds by netting the third.
Elsewhere, another ex-Heracles player scored a hat-trick as Mark Uth grabbed all of Hereenveen's goals in their 3-1 win over Utrecht, and Cambuur overcame Den Haag 3-2.