The Suns moved past Utah into ninth place in the Western Conference, a game out of the final post-season spot.
Phoenix had as much as a 13-point lead in the fourth quarter before Al Jefferson tied it for the Jazz with 9 seconds to play.
A study of the video replay, however, caused officials to negate Millsap's basket and leave Phoenix with its third straight win.
Utah was paced by 25 points from Millsap and 22 from Miles. Utah has lost four out of five.