Left-back Rajko Brezancic, making his debut after signing from Serbian side Cukaricki, got AZ on the board early after his long-range shot took a wicked deflection to loop over Hidde Jurjus and settle in the net.
Nathaniel Will equalised for Graafschap with a stunning effort into the top corner on the stroke of half time.
Midfielder Henriksen then got his two goals in quick succession halfway through the second half to put AZ in the driving seat.
Chances came few and far between for both teams after that and the scoreline stayed 3-1 until the final whistle.
The result sees AZ move up into 12th position in the league while Graafschap remain point-less.