Evan Turner (10 points) put the 76ers ahead for good on a driving layup with 40 seconds remaining and added a pair of free throws down the stretch for Philadelphia, which leveled the best-of-seven series at one win apiece.
Andre Iguodala chipped in with 13 points, seven assists and six rebounds while Lavoy Allen contributed 10 points and eight boards as the Sixers won a playoff game in Boston for the first time since 1982.
Kevin Garnett finished with 15 points and 12 rebounds but committed a key offensive foul in the final seconds for the Celtics, who were outrebounded 47-36 in the loss.
Game 3 is set for Wednesday at Philadelphia.
Swim Week Miami Beach 2014 [PHOTOS]