The Jazz started well and, less than four minutes into the game, they owned a 10-5 lead.
Denver's offensive rebounding stopped Utah's early momentum, however, and the Nuggets took a 21-19 on Andre Miller's layup with 1:34 remaining in the first quarter.
On the Jazz's next two possessions, though, Derrick Favors hit two free throws and a converted a drive into a spectacular left-handed dunk as Utah claimed a 23-21 lead.
Backup point guard Earl Watson got the Jazz going in the second quarter.
After scoring four points in the previous five games, Watson hit a floater from the lane and a 3-pointer on back-to-back possessions.
Utah gradually built a 36-31 lead and had two chances to extend its advantage. But the Jazz couldn't do it and Gallinari made them pay.
After struggling lately, Gallinari scored eight points in the final 6:10 and the Nuggets finished on an 18-9 run to take a 49-45 lead.
In the third quarter, Denver opened with two baskets to make it 53-45.
After a Gallinari jumper, Millsap's inbounds pass was stolen by Ty Lawson, whose steal and layup highlighted an 11-2 run that made it 60-47.
The Jazz countered with nine straight points of their own, but the Nuggets converted seven of their next eight possessions to regain control.
It was 83-72 heading into the fourth quarter, which it the Nuggets dominated.