The Netherlands and Milan legend made the switch to the Alkmaar club during the close-season after guiding Heerenveen to a commendable fifth-placed finish last term and he got the start he craved in Almelo.
Heracles kept things tight during the first half and went into the break level but AZ soon took the lead as Steven Berghuis netted in the 56th minute.
Guus Hupperts doubled the deficit seven minutes later and former Fulham man Muamer Tankovic completed the scoring with just over quarter-of-an-hour to go.
Eredivisie newcomers Dordrecht picked up an impressive win upon their return to the Dutch top flight, beating Heerenveen 2-1 away from home in the season's first shock.
Hakim Ziyech got the hosts off to a good start as he found the net in the 14th minute but Dordrecht equalised through Giovanni Korte a few moments before the break.
The travelling fans were made to wait but Dordrecht did eventually get the all-important winner through Joris van Overeem, securing victory in the side's first Eredivisie match since 1995.
Twente endured a somewhat disappointing opening day as they drew 1-1 at Cambuur but it could have been much worse as Youness Mokhtar rescued a point with his 88th-minute equaliser, while Excelsior held NAC Breda to a 1-1 draw.
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