Utah were comfortably in front 73-52 late in the third quarter when the visiting Wizards stormed back with a 20-2 run that put the pressure on the Jazz in the fourth.
However, Gordon Hayward scored three straight points, finishing with 15, after the challengers had pulled within two and Utah made their free throws down the stretch to seal the game.
Paul Millsap led the home side with 16 points and 15 rebounds while team mate Al Jefferson also notched a double-double.
Though the Wizards (9-31) have the NBA's worst record, they have been boosted by John Wall's return from a knee injury and are 4-3 since he joined the team.
He had 14 and eight assists against the Jazz (23-19) and Martell Webster recorded 15 in the loss.