Neither team shot more than 39 percent from the floor and the Lakers could make only 1-of-15 from 3-point range, but the old rivals played a close, tense contest that was not decided until Boston's Paul Pierce and Ray Allen both missed jump shots in the final 3 seconds.
The Celtics took an 87-86 lead with 1:46 to go in the extra period on a 3-pointer by Pierce, after which Kobe Bryant put up a jumper for the Lakers. That shot missed, but Bynum was there for the tip-in.
Boston then missed its final four shots, two of them from Kevin Garnett. The Celtics had a five-game winning streak snapped.
Los Angeles also scored the last points of regulation, those coming on a layup by Pau Gasol that tied it at 82-82 with 10 seconds remaining. Mickael Pietrus missed a 3-point try for the Celtics at the fourth-quarter buzzer.
The Lakers ended a two-game skid and improved to 2-2 on a six-game road trip that has stops remaining in New York and Toronto.
Bryant scored 27 points on 24 shots to lead the Lakers. Gasol scored 25 and Bynum had 15. Allen tallied 22 points and Pierce had 18 for the Celtics.