Gallinari scored on 3-of-10 attempts from 3-point range and also collected nine rebounds in Denver's third consecutive win and seventh at home.
Faried rounded out his double-double with 11 of Denver's 58 team rebounds. Kosta Koufos had 14 boards.
Tim Duncan held up San Antonio's end in the paint with 18 rebounds to go with his 31 points and six assists. It wasn't enough for the Spurs, who lost for the fourth time in their last five games.
Denver dominated the middle two quarters and led 90-75 heading into the fourth quarter. The Nuggets wound up needing that cushion as the Spurs rallied and outscored their hosts 31-22.