Johnson hit 10-of-16 from the field, including four from beyond the 3-point arc, and handed out six assists in the Nets' third win in their last four games.
Alec Burks scored 23 to lead the Jazz, who had their three-game win streak ended. Enes Canter scored 18 and Trey Burke 14.
The game was tied 84-84 when Brooklyn erupted with a 15-5 run that put the Nets ahead 99-89 with 1:51 left in the game.
Notable deaths of 2014 [PHOTOS]