LeBron James is averaging 23.8 points and 6.9 assists for the Cavaliers, who have won seven of eight.
The Celtics are in third place in the Eastern Conference, just behind Cleveland.
Boston led the Cavaliers in scoring and rebounds for much of the first half, but were outrebounded 38-34.
The Cavs led by as many as 14 points in the third quarter.
The Cavs led 51-39 at halftime, and led by 10 in the fourth quarter before James led the Celtics to a 74-64 lead on a layup with 5:33 left.
James led the Cavs with 20 points and nine assists, while Kyrie Irving added 17 points and 11 rebounds for the Celtics.
James was 6 for 13 from the field and 7 for 10 from the foul line for the game.
Irving was 6 of 9 from the floor and 5 of 10 from 3-point range.
James is averaging 29.2 points, 9.9 rebounds, 6.8 assists and 3.3 steals per game.