Rajon Rondo had 17 assists, 13 points and 12 rebounds for his eighth career playoff triple-double. He ran the length of the court to receive the inbounds pass and dribble out the final 3.4 seconds of the game.
Game 2 is Monday night in Boston before the series shifts to Philadelphia for Games 3 and 4.
Andre Iguodala scored 19 points and Evan Turner had 16 points and 10 rebounds for the 76ers, who advanced to the second round for the first time since 2003 by beating East No. 1 seed Chicago.
The Sixers led 77-67 with 11 minutes to play before Boston scored 23 of the next 30 points.
Paul Pierce, who had a sprained MCL in his left knee, scored 14 points on 3-for-11 shooting for the Celtics.
Rondo was only 6 for 15 from the floor, but he was 3 for 6 in the fourth quarter, adding five rebounds and four assists.