Irving, who played only 11 games at Duke before being drafted first overall, topped his previous high of 21.
Anderson Varejeo contributed 15 rebounds for the Cavaliers.
Steve Nash led six Suns players in double figures with 16 points, becoming the 15th active player to reach 16,000 points. He also had 15 assists. Marcin Gortat had 14 points and 12 rebounds for Phoenix.
Michael Redd, playing his first game for Phoenix, had 12 points in 19 minutes.
Irving put on a remarkable performance in the first half. With the Cavaliers trailing 40-34, he scored 12 consecutive points in 2:51, including two 3s, capping a 14-0 run and lifting Cleveland to a 46-40 advantage. Irving did his damage against Nash, the league's two-time Most Valuable Player.
After Irving's offensive outburst, Jamison took charge of the offense. He scored seven straight Cleveland points, helping the Cavaliers to a 56-48 halftime advantage.
Irving finished the half with 16 points and Jamison had 13.
The Cavaliers, in the midst of a tough trip, played with extreme energy in the first half, outrunning and outrebounding the Suns.
Redd made his Suns' debut early in the first period, replacing Grant Hill, who had to leave with a bloody nose. Redd hit his first two shots, both 3s, then finished the half by shooting 3 for 6 in 10:55. Redd, signed recently as a free agent had not played since last April, but only sparingly with the Milwaukee Bucks. Because of two knee surgeries, he had played in only 61 games in the past three seasons.
Hill later returned, but experienced soreness in his right knee and did not play in the second half.
Both teams continued to fire up 3-pointers in the first half, the Suns taking 14 from long range and the Cavaliers 11.
Jamison and Irving continued to spearhead the Cavaliers' offense in the third period. Jamison had 10 points in the quarter and Irving had six as Cleveland retained its eight-point lead, 79-71. The Suns never got closer than six points in the fourth quarter.
The teams had battled to a 30-30 tie in the first period, the 30 points for Cleveland representing the most against the Suns in the opening quarter this season.
NOTES: This was the Cavaliers' fifth game in a gruelling seven-game trip. They began it by losing to Toronto, then beat Minnesota, and lost to Utah and Portland. They will conclude the long journey with games at the Los Angeles Lakers and Charlotte. ... The Suns host New Jersey on Friday night, then embark on a five-game trip, starting with San Antonio and followed by Chicago, New York, Boston and Dallas. ... Cleveland is one of the youngest teams in the league with seven players with one or fewer years of NBA experience. ... The court at US Airways Center was refinished since the Suns last played on it Sunday night. The refinishing was necessary because players were slipping on it.