Guard Lafayette Lever scored six of his 22 points in overtime, leading host Denver to a 2-0 lead in its best-of-seven Western Conference semifinal series with Utah.
Games 3 is Saturday afternoon in Salt Lake City.
The Nuggets twice rallied from seven-point deficits in the final quarter, taking advantage of cold shooting by Utah.
After Adrian Dantley's three-point play gave the Jazz a 110-103 lead with 7:21 remaining, Utah went nearly three minutes without a point while the Nuggets scored 10 straight.
Rickey Green's three-point play drew Utah into a 117-117 tie with 3:27 left, and Denver's Calvin Natt and Utah's Thurl Bailey exchanged free throws to account for the 119-119 tie at the end of regulation.
Denver center Wayne Cooper hit two long-range jumpers early in overtime, and a Lever basket with 3:20 remaining in overtime put Denver ahead, 127-123.
While Utah suffered from turnovers and misses, Lever sank four free throws in the closing minute to secure the victory.
Alex English had 26 points, Natt 24 and Cooper 16 for Denver. Green paced Utah with 25 points, while Dantley and Jeff Wilkins had 20 each.