Gallinari made 7-of-11 shots from 3-point range and scored 39 points. He also had eight rebounds, as did Andre Iguodala to go with his 20 points.
Denver scored the final five points of the second period to take a seven-point advantage at halftime, then dominated the third period while handing the Mavericks their fifth straight loss.
O.J. Mayo led Dallas with 15 points.