The outcome spoiled the return to action for Minnesota's Kevin Love, who made his season debut after breaking his right hand prior to the start of the campaign.
Minnesota held a 14-point lead at halftime and was still in front by four heading into the closing period. Denver took the lead for good at 90-87 on a 3-pointer by Ty Lawson with 4:02 to play.
Gallinari hit 6-of-11 from the floor and scored 19 points. Andre Iguodala added 18 points for the Nuggets and Lawson had 18 points to go with nine assists.
Love scored 34 points with 14 rebounds, but the Timberwolves lost for the fourth time in five games.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut