Phoenix won for the sixth time in seven games, overcoming a first-half road deficit to move within two games of the lead in the Pacific Division.
Dragic hit two foul shots to give the Suns a 99-97 lead and his layup with 1:01 remaining boosted the advantage to four.
The only points Denver could produce over the final three minutes came on a dunk by JJ Hickson with 19 seconds to play.
Six Denver players reached double figures in scoring, but none could produce more than the 15 delivered by Wilson Chandler.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes