The Jazz jumped past Phoenix into ninth place in the Western Division playoff race, having begun the night only 1 1/2 games out of a post-season position.
Jefferson scored 30 points and grabbed 11 rebounds. Harris' 28 points were a season best and came after he had missed Utah's previous game with an ankle injury.
Utah has won two straight after suffering through a three-game skid.
David Lee led Golden State with 26 points and 12 rebounds. Klay Thompson had 23 points.