The USA striker had a huge day for AZ, netting three times as his club took home three points.
The match went to the break still scoreless, but 10 minutes after halftime Altidore put his team on the board with a header into an open net after being found by a brilliant chipped cross.
His second goal came in similar fashion, with Altidore unleashing a diving header to make it 3-0 in the 64th minute after Roy Beerens had made it 2-0 two minutes earlier.
In the 77th minute, Altidore rounded out his and AZ's night after controlling a lovely driven cross and then smashing home to round out his hat trick. The goal was Altidore's 14th in the Eredivisie this season, tied for second overall.
Vitesse pulled one back in the 83rd, but AZ would cruise to a comfortable 4-1 win despite conceding the consolation goal.