Deron Williams added 19 points and seven assists. His 3-pointer with 2:11 remaining gave the Nets their largest lead of the game.
Brooklyn snapped a three-game road losing skid and the surging Nets have won five of their last seven contests.
Reserve guard Alec Burks led the Jazz with 23 points and Enes Kanter, starting in place of Derrick Favors (hip), had 18 points and 10 rebounds, but the Jazz wasted a 13-point third-quarter lead and a chance to extend their winning streak to a season-best four games.
The Nets completed their first season sweep of Utah since 2006-07, but it may prove costly just two games into their seven-stop road trip.
Paul Pierce, who had seven points in 27 minutes and didn't play in crunch time, was limping after the first sequence of the second half and called a time out so he could leave the court. His left leg or foot seemed to be bothering him and he immediately hobbled to the locker room with 11:11 left in the third quarter. He returned a few minutes later but was ineffective.
The Nets acquired guard Marcus Thornton from the Sacramento Kings for Jason Terry and Reggie Evans on Wednesday, but Thornton hadn't yet joined the team at game time so the team was short-handed.
But just when the Nets looked buried, they found a spark.
The Jazz led 68-55 after Gordon Hayward and Richard Jefferson made back-to-back 3-pointers. Johnson had seven points in a 20-4 run that culminated in Blatche's jumper that gave the Nets a 75-72 lead just before the end of the third quarter.
In the final period, the Jazz battled back within 89-88, but Williams started the game-deciding run with a jumper and capped it with his big 3-pointer and the Jazz couldn't get within four points the rest of the way. It was a memorable night for Williams, who struggled to 9-for-29 shooting in his first two games in Salt Lake City after being traded from the Jazz to the Nets in 2011 but made the big shots in this one.
Favors has been bothered by a sprained right hip he hurt against Detroit on Jan. 17. He originally sat out just one game, but he has aggravated the hip twice and this will mark the fifth game missed due to the injury.
Though the Jazz outrebounded the Nets 46-33 without Favors, the Nets shots 50 percent and outscored Utah in the paint 48-40. Utah dropped to 0-6 without Favors and just 1-22 when Kanter starts.
Jeremy Evans had a career-high 13 rebounds for the Jazz in just 20 minutes of play.