Phoenix has won back-to-back games for only the second time this year. The Suns' latest two-game winning streak comes on the heels of seven straight losses.
Utah, which had won its four previous outings, has a 9-1 home record but is only 4-10 on the road.
Dudley scored 22 points and led the Jazz to a 34-22 lead after one period. Utah was within eight points heading into the game's final nine minutes, but the Suns pulled away down the stretch.
Goran Dragic added 18 points for Phoenix and Marcin Gortat had 12 points and 14 rebounds.