Ray Allen, a former Connecticut standout, scored 16 points for the Celtics (3-1) and James Posey added 12 points.
Boston coach Doc Rivers rested stars Pierce and Garnett with back-to-back exhibition games against New York and New Jersey scheduled on Monday and Tuesday.
With the Celtics trailing by 10 at halftime, Allen scored five straight points to spark a 16-4 run to open the second half. Brian Scalabrine hit two shots in a row from the corner and Rajon Rondo converted a short jumper to put the Celtics ahead 56-54 with 6:57 remaining in the third quarter.
Reggie Evans made two free throws to give Philadelphia the lead for good, 61-60, with 3:59 remaining in the period. The 76ers led for nearly the entire game, jumping to a 25-15 lead by the end of the first quarter and 50-40 at halftime.