Irving, who became the No. 1 draft pick in the NBA this season despite a limited career at Duke, hit 11-of-17 shots from the field while Antawn Jamison was adding 23 points.
The Cavaliers ended a two-game skid and improved to 2-3 on a seven-game road trip that has meetings remaining with the Los Angeles Lakers and Charlotte. Cleveland has split its first 10 games of the season after winning only 23 percent of its contests a year ago.
Steve Nash had 16 points and 15 assists for the Suns, who had won their three previous home games.
Irving, who has scored at least 20 points in three straight games, boosted Cleveland to an eight-point lead at the half.