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.
"I would say we were tense," Utah's Gordon Hayward said. "We go a little too fast and we start missing shots and they were able to get good lucks."
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.
Wall had 14 and eight assists against the Jazz (23-19) and Martell Webster recorded 15 in the loss.
After being dominated early and trailing by 21 in the second, Washington was able to make it a test down the stretch as they finished 2-3 on their five-game road trip.
"It was a good fight-back by us, but just a bad job of coming out and being ready to play," said Wizards guard A.J. Price.
"If we had come up from the start and been ready to play it probably would have been a different game."