The Celtics led by 22 points at one point, but the Cavaliers narrowed it to two with a minute remaining.
Kevin Garnett turned back the Cleveland rally with a fadeaway jumper and Boston barely managed to post a win and earn a split in its home-and-home series with the Cavs.
The Celtics had also blown a sizable fourth-quarter lead in Sunday's first game, ultimately losing to the Cavs 88-87 on Kyrie Irving's layup with 2.6 seconds left.
Garnett and Brandon Bass each finished with 13 points as Boston notched its fifth victory in six games.
Irving collected 21 points while Anderson Varejao added 20 points and 20 rebounds for Cleveland.