The visitors took the lead in spectacular fashion in the 11th minute when Markus Henriksen headed the ball back into the six-yard box from a corner and Wesley Hoedt met it with an overhead kick, which flew past Nick Marsman into the net.
AZ doubled their lead in the 34th minute with a well-worked moved down the right as Mattias Johansson exchanged a one-two with Steven Berghuis, before crossing into the middle for Aron Johansson to fire an effort past Marsman from close range.
In the second half, Twente pushed to get back into the game, but the visitors remained in control of the match with a strong possession game.
However, AZ were reduced to 10 men when midfielder Nemanja Gudelj was sent off for his second bookable offence in the 69th minute to give the home side hope of getting back into the game.
Twente pushed forward in numbers, but were unable to break through the resilient defensive line of the visitors as John van den Brom's men held out for the three points.