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The visitors had the first attempt on goal of the evening, but Marten de Roon's strike lacked the power to beat the keeper.
They continued to create the better of the chances and Jordy Buijs came close with a curling effort.
Daley Sinkgraven gave the visitors the lead towards the end of the first half when he swept a low shot into the bottom corner, after the ball had broken kindly to him inside the box.
After the break, Robert Muhren twice came close for AZ when he headed wide and saw a strike go just past the post.
The hosts continued to push for an equaliser, but they could not find the net as they fell to a third loss of the league season.