The Nuggets had a chance to tie it with 3.6 seconds left but Ty Lawson was double-teamed and passed too late for Corey Brewer to get off a final shot.
The Jazz, who improved to 6-0 at home, trailed by as many as 16 in the first half and were down 12 with 7:27 left in the third before going on a 14-2 run to tie it at 77.
The Nuggets played the rest of the way without Andre Iguodala, who was ejected with 3:24 left in the third. He had 10 points, three rebounds and three turnovers.
Favors added a season-high 19 points and seven rebounds, including two in the final minute.
Kenneth Faried led Denver with 21 points.
Lawson added 16 points for the Nuggets, but shot just 7 of 17.
The Nuggets held a 48-18 advantage on points in the paint at halftime but had just 18 the rest of the way as the Jazz buckled down and started playing defense.
The game turned in the third quarter, usually the Nuggets best quarter in recent games as they were riding a four-game winning streak.
Down 12, the Jazz went on their own run, with back-to-back 3-pointers by Randy Foye and Marvin Williams tying it at 77.
Foye then tied up Iguodala on the next possession, and won the jump, leaving Iguodala complaining.
When JaVale McGee was called for a foul on Paul Millsap at the other end, Iguodala complained again and picked up his first technical. He received his second after Foye made the free throw, sending him out of the game for good.
The Nuggets hung tough, nonetheless, sending the game into the fourth quarter tied at 84.
Favors' jam over McGee gave Utah a 91-89 lead, and Faried answered at the other end.
Another dunk by Favors put Utah ahead 97-93 but Faried and Lawson kept the Nuggets in it, with back-to-back baskets to tie it at 100.
Jefferson's free throws gave Utah a 102-100 lead and Andre Miller tied it with 54 seconds left. But after a miss by Jefferson at the other end, Favors was there for the offensive rebound, and made both free throws after getting fouled..
Favors grabbed another rebound after Miller missed a 3-point attempt with 5.9 seconds left, and sank one of two from the line.
Favors finished with 19 points, seven rebounds and two blocks.
Tinsley, who started in place of injured Mo Williams for the second straight game, contributed a season-high 15 points on 6-of-9 shooting, including 3 of 6 from 3-point range.
The first half was pretty much all Denver as the Nuggets shot 73 percent and led by as many as 16 points in the second quarter.
Denver led 65-54 at the half.