Dragic connected for 21 points with seven assists while Brown came off the bench to fire in 19 as the Suns claimed a win for the third time in four games.
Michael Beasley helped out with 16 points and Markieff Morris (13 points, six rebounds, five assists) perpetrated a key steal with 2:16 left in the game for Phoenix.
The Nuggets, meanwhile, saw their four-game winning streak snapped despite 17 points and nine rebounds from Andre Iguodala.
JaVale McGee supplied 16 points in Denver's loss.
Boston schools pull out free condoms over wrapping complaints
NBC reportedly holds celebs hostage to Jimmy Fallon's show