Mo Williams totaled 19 points and six assists as Utah escaped with a 92-90 victory over Brooklyn at Barclays Center.
Al Jefferson contributed 16 points and 11 rebounds, while Derrick Favors picked up 13 points for the Jazz, who began a four-game road trip by snapping a two-game slide.
Joe Johnson recorded a game-high 21 points and Brook Lopez had 16 for the Nets, who have lost two in a row and seven of their last nine.
"This is a tough loss," said Nets guard Deron Williams, who totaled 14 points and five assists in defeat. "We have to bounce back."
The Jazz finally took the lead for good on a Mo Williams trey with 5:42 remaining in regulation. Favors added a jumper to make it 84-80 for the visitors and they held the hosts at bay from there.
Lopez closed the gap to two from the charity stripe, but Mo Williams connected to restore the four-point margin for the visitors. After a Deron Williams reverse layup, Gordon Hayward countered for Utah. Deron Williams came back with another bucket in the paint for Brooklyn, and Jefferson answered for a 90-86 game.
Lopez hit two more from the line, but Jefferson nailed a jumper with 1:36 left for a 92-88 spread. Following a Utah turnover, Favors fouled Johnson on a layup try, and he converted both with 22.1 ticks showing.
Jefferson then lost the ball on an inbounds play to Johnson, who worked a quick passing play to Gerald Wallace, who missed a three-pointer. Reggie Evans grabbed the rebound but missed his shot from in close in the final second.
"We did a lot of great things in the second half," Mo Williams said. "We had to dig down deep."
A Lopez 3-point play made it 12-6 for the hosts just under three minutes in, then Utah pulled within 20-18 on a Paul Millsap layup. Thanks to a Deron Williams jumper, the Nets led 24-20 after one quarter.
DeMarre Carroll's slam pulled the Jazz ahead 30-29, but a 16-2 run thereafter helped push Brooklyn's lead to 45-32. CJ Watson and Johnson each drained a trey during the surge which ended on a Lopez bucket with just over five minutes left in the first half.
Wallace connected from long distance on the final shot of the quarter and the hosts led 57-44.
The Nets led 65-56 in the early stages of the third period thanks to a Johnson floater, but the Jazz crawled back within 69-68 on a Favors alley-oop slam. It was 74-70 for the hosts heading to the fourth after a dunk from Andray Blatche and a trey from Johnson.
Utah has won six of the last seven meetings ... Kris Humphries notched 11 rebounds with eight points in 28-plus minutes for Brooklyn ... Millsap had 12 points, eight rebounds and three steals, while Marvin Williams clocked in with 11 points and 10 boards for the victorious Jazz ... Utah continues its road swing at Indiana on Wednesday.