However, the bigger loss for Boston was new forward Gordon Hayward, who fractured his left ankle in the first period.
The injury occurred when Hayward was bumped in the air by LeBron James and fell with his leg pinned under him in the first quarter.
Hayward, 27, who signed a four-year, $128 million contract in the offseason with the Celtics, immediately called for help with his foot and ankle dangling in the wrong direction.
The Celtics huddled in prayer and new teammate Irving had to be consoled while medical personnel stabilized Hayward's leg. Hayward was carried off the court on a stretcher.
Cleveland led by as many as 18 points in the third quarter, but the Celtics rallied to take a four-point lead with a little over four minutes left. However, Boston scored just one point in the final two minutes.
James finished with 29 points, 16 rebounds and nine assists after missing most of the preseason with a left ankle sprain.
Irving, who requested a trade away from James and the Cavs in the offseason and was dealt to the Celtics, finished with 22 points and 10 assists in his return to Cleveland.
Derrick Rose scored 14 points in his Cleveland debut, while Dwyane Wade added eight points in his first game for the Cavs. Kevin Love finished with 15 points and 11 boards, and he made a 3-pointer on a pass from James with 46.3 seconds left that proved to be the difference.
Second-year player Jaylen Brown paced the Celtics with 25 points.
Irving asked to be traded from the Cavs in July, and on Aug. 22, he was shipped to Boston for Isaiah Thomas, Jae Crowder, Ante Zizic and two draft picks.
NOTES: The Cavs canceled a planned video tribute honoring former Cavs and current Celtics G Kyrie Irving, according to cleveland.com. ... Irving said he wasn't comparing Cleveland in a negative way to Boston when he said his new home was a "real, live sports city." Irving said, "I was talking about driving into Boston. When I'm actually on the highway driving into Boston, the newness and the new environment of going into that city is something different for me." He said, "My love will never change that I have for Cleveland." ... Cavs G Dwyane Wade said F LeBron James' first game back in Cleveland as a member of the Miami Heat "was a movie." On Dec. 2, 2010, James returned to Quicken Loans Arena and dropped 38 points in three quarters on his old team... James needs four more games to pass Zydrunas Ilgauskas (771 games) for the most in Cavs' franchise history.