The side slipped to an unlucky opening day defeat against Willem II but avenged that loss in style on Friday evening.
Jan Kromkamp had the Almaarderhout Stadion side ahead 18 minutes in, but they had to wait until the second period before the floodgates opened.
Despite a spirited effort from Twente, Robin Nelisse doubled AZ's advantage just after the hour mark to all but seal the three points.
With the home side controlling proceedings, Ali Elkhattabi netted late on to put the icing on the cake.
The visitor's night was compunded after referee Dick Van Egmond dismissed Adil Ramzi, leaving them to finish the match with ten men.
Click below for Dutch match summary:
AZ Alkmaar 3-0 FC Twente
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