The American striker scored in the 14th minute, adding to Adam Maher's opener minutes earlier, as AZ clinched their first cup since 1982.
Altidore, who has now scored a total of 31 goals this season, was over the moon in the wake of the victory in what has been a successful campaign both personally and from a team perspective.
"Of course, any time you can be a champion, [the season is a success]," Altidore told MLSsoccer.com.
"I'm just so happy to win something. I told the guys, it's not every day you get in this position.
"You never know - I may never get this chance again in my career. It's been a tough season, with a lot of ups and downs, but it's great to win a championship."