Marcus Smart added 31 points and Gordon Hayward finished with 21 points and 13 rebounds. Kemba Walker added 19 points and nine rebounds. Tatum and Smart combined for 16 of Boston’s 27 points in the overtime periods.
The Celtics have won seven straight at home and eight of their last nine overall.
The Clippers played most of the game without Paul George, who left in the second quarter with a left hamstring strain. Lou Williams led Los Angeles with 35 points. Kawhi Leonard had 28 points and 11 rebounds, and Montrezl Harrell finished with 24 points and 13 rebounds.
George played 15 minutes, scoring four points on 2-of-7 shooting before heading to the locker room.
The first meeting between the teams on Nov. 20 was also decided in overtime. The Clippers held on for a 107-104 win.
The Celtics took a 134-130 lead in the second OT on a driving layup by Smart and another by Tatum.
Harrell got a dunk on the Clippers’ next trip up the floor. But Hayward responded with a 3 to increase Boston’s lead to 137-132.
Tatum was called for an offensive foul, but Hayward blocked a runner by Williams off his body to force the turnover with 55 seconds left.
Hayward hit four free throws in the final minute to help close it out.
The All-Star break comes at a perfect time for both teams as they try to get healthy.
Smart started in place of Brown and scored the Celtics’ first 10 points, digging them out of an early 7-0 deficit. Smart and Tatum combined for 24 of Boston’s 30 first-quarter points. It helped offset a 15-point opening period by Leonard.
Boston limited Leonard to two points in the second quarter but had no answers on the inside for Harrell, who had 16 points in the first half on 5-of-5 shooting from the field.