The Celtics seized a 3-0 lead in the best-of-seven second-round series and could complete a sweep of the 76ers by winning game four Monday at Philadelphia.
Jaylen Brown came off the bench to add 16 points for the Celtics while Al Horford contributed 13 points and Australian Aron Baynes grabbed 10 rebounds.
Joel Embiid had 22 points and 19 rebounds to lead the 76ers, while J.J. Redick added 18 points and Aussie playmaker Ben Simmons contributed 16 points, eight rebounds and eight assists.
A steal by Rozier set up a basket by Brown that gave the Celtics an 89-87 lead with 1.8 seconds remaining in regulation time, but the 76ers equalized when Italy's Marco Belinelli sank a jumper off a pass from Simmons with 0.3 of a second remaining, sending the contest into overtime.
A Belinelli basket and Redick 3-pointer put the Sixers up 94-87, but the Celtics closed on a 12-4 run, Horford scoring the final five points to bring Boston the victory.