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.
THUNDER 123, PELICANS 118
NEW ORLEANS (AP) — Danilo Gallinari scored 29 points, Chris Paul had 14 points and 12 assists, and Oklahoma City beat New Orleans.
Zion Williamson scored 32 points for New Orleans, his second straight game scoring more than 30, but Gallinari's clutch shooting — he had 11 points in the fourth quarter — kept the Pelicans at bay.
New Orleans, which trailed by as many as 13 points in the third quarter, rallied behind Williamson's dominant inside play to take several slim leads inside the final six minutes.
But after Lonzo Ball's corner 3 gave the Pelicans a 111-110 lead, Gallinari hit a fall-away in the paint and followed up by rattling in a 3.
Dennis Schroder scored 22 points for the Thunder and Shai Gilgeous-Alexander added 17 points.
JJ Redick scored 24 points for the Pelicans, who saw their three-game winning streak snapped.