The Sixers had previously grabbed game two in Boston to knot the series at one game apiece.
In a game that neither team led by more than 10 points, the Celtics took a five-point lead into the fourth quarter as Jayson Tatum and Jaylen Brown scored 25 points apiece to lead the Celtics.
Tyrese Maxey's three-pointer briefly put the Sixers up 85-84 with 8:42 remaining, and Philadelphia were within one when Tatum drilled a three-pointer that pushed Boston's lead to 100-96 with 1:57 left to play.
Payton Pritchard added another three-pointer with the shot-clock winding down before Tatum - who missed most of the season after suffering a torn Achilles tendon in last year's playoffs - drained a dagger trey that sealed it for Boston.
"We just were resilient," Tatum told broadcaster Prime. "We stuck with it. It's a game of runs - good team and just, you've got to answer."
Maxey scored 31 points to lead the Sixers. Paul George added 18, and rookie VJ Edgecombe added 10 points and 10 rebounds.
Sixers star Joel Embiid, still recovering from an emergency appendectomy earlier this month, was ruled out shortly before the game.
"He's just not ready," said Sixers coach Nick Nurse, whose team will try to even the series when they host game four on Sunday.