Kanter made 11 of 13 shots and the Jazz overcame a 13-point deficit to take control in the fourth quarter and keep the Wizards from moving above the .500 mark for the first time in more than four years.
Hayward finished with 16 points, Alec Burks added 15 and Derrick Favors had 11 points and 14 rebounds after a one-game absence.
Trevor Ariza led Washington with 23 points, including a 3-pointer with 52 seconds left that got the Wizards within 101-98. He and Bradley Beal both missed 3-point attempts to tie the game on the next two possessions.
John Wall banked in a 3-pointer to get within 102-101 with 3.6 seconds left, but Hayward made two free throws and Wall missed at the buzzer.
Kanter scored a total of eight points in two blowout losses to Minnesota and drew his coach's ire for often being in the wrong spots. But in this one, Kanter consistently found himself in the right place at the right time - picking up loose balls, making timely passes and changing the Wizards' shots in the paint.
The muscular center from Turkey displayed a deft shooting touch on jumpers and power moves to the basket. When Ariza's 3-pointer cut the lead to 92-90, Kanter hit a jump shot. With 57 seconds left, he made two free throws to give Utah a 101-95 cushion after a nifty reverse-pivot down the lane that drew a foul.
Burks and Hayward drove through the Wizards' defense for layups as the Jazz scored on four straight possessions to open the fourth quarter and take an 85-77 lead.
The Jazz seemed a step quicker to loose balls as the game wore on, but the Wizards made it interesting in the final minute before yet again failing to move above .500.
Ten times over the past five seasons, the Wizards have had a chance to surpass .500. They've lost every time.
Wizards last won a game to go above .500 on Oct. 31, 2009, when they beat the New Jersey Nets to improve to 2-1. They lost to Cleveland on Nov. 3 and haven't had a winning record since.
The Wizards, who led most of the game, have lost this season at 0-0, 9-9, 14-14, 19-19, 20-20 and 21-21. No one on the current Wizards roster was on the team when it was last above .500.
Though Utah is at the bottom of the Western Conference standings, the Jazz are competitive when healthy. The starting lineup of Trey Burke, Hayward, Marvin Williams, Richard Jefferson and Favors is 12-8 this season.
Favors was a game-time decision but felt his right hip strain had healed enough to give it a go and the Jazz needed his presence inside. When Favors needed a rest, Kanter made his presence known, especially with his 10 points in the fourth quarter.
After stumbling through a subpar January, Ariza has found his groove. He scored 23 points in a win over Phoenix Friday and made 6 of 10 3-pointers against Utah.
But his fellow perimeter players couldn't find their range. Beal was 5 of 16 and Wall made just 4 of 14 attempts from the field.
Nene had 19 points, including a handful of emphatic dunks, and Marcin Gortat had 14 points and 11 rebounds, but they couldn't stop Kanter when it mattered most.