Kanter connected on 11-of-13 shots from the floor for the Jazz, who secured the win when the Wizards' John Wall missed a desperation 3-pointer at the final buzzer.
Gordon Hayward put in 16 points and Alec Burks added 15.
Derrick Favors had 11 points and 14 rebounds and Trey Burke added 12 points and eight assists as Utah broke a two-game losing streak.
Washington got 23 points from Trevor Ariza and 19 from Nene.
Marcin Gortat had 14 points and 11 rebounds.