The Suns survived a last-second 3-point miss by Kyrie Irving to win a game in which they trailed by as many as 18 points in the first half.
Dragic made 1-of-2 foul shots with 18 seconds left to put Phoenix in front by four points, but Daniel Gibson hit a 3-pointer for the Cavaliers to bring the Cavaliers within one with 13 seconds remaining.
Telfair was then fouled and he could make only 1-of-2 as well, leaving Cleveland with a chance to win the game. Irving's attempt to do so misfired, giving the Cavaliers their second straight loss.
Dragic scored 26 points and Shannon Brown chipped in 22 off the bench.
Cleveland was led by rookie Dion Waiters with 23 points. Irving had 17 points and eight rebounds.