The Sixers led by 10 points and controlled the Eastern Conference-leading Celtics for most of the fourth quarter.
The Celtics missed eight straight baskets over a six-minute span late in the fourth to lose only their eighth conference game of the season.
Lou Williams' jumper just a shade over the five-minute mark put the Sixers ahead 83-81 and they never trailed again. Jodie Meeks made two free throws after he was hammered by Paul Pierce on a fast break attempt and the Sixers came away with one of their biggest wins of the season.
Nenad Krstic had 16 points and 15 rebounds for the Celtics.
Andre Iguodala had 13 points, nine rebounds and eight assists for the Sixers. Meeks scored 12 and Thaddeus Young 11.
The Celtics took their final lead on Ray Allen's 3-pointer with 6:27 left in the fourth to make it 81-79. That was it from the floor until Kevin Garnett scored a bucket in the final seconds.
It was an off night for the Big Three: Garnett scored 14 points, Pierce had 11 and Allen five. Jeff Green led Boston with 18 points.
The Sixers left the court to a rousing standing ovation. The sellout crowd, with several pockets colored with Celtics green, was standing from the start for this potential first-round playoff series.
The Sixers play the next five games on the road, a pivotal stretch for the improving team.
Celtics coach Doc Rivers said before the game he'd take special note of this one because of the postseason implications.
"I don't know if you put more into the game, but you take more out of the game," he said.
Celtics-Sixers once was one of the NBA's fiercest rivalries. While the series has cooled over the years as the Sixers slid into mediocrity, the atmosphere was hot from the opening tip.
Sixers chairman Ed Snider popped up from his courtside seat, waving his arms in protest over a non-call against his team. When Brand, who needed X-rays on his sore left hand, grabbed a defensive rebound and finished on the other end with a monster dunk, there was an enthusiastic roar.
The Sixers led 49-45 at halftime and never trailed Boston by more than two points the rest of the way.
Notes
Rivers expects Glen Davis (strained left patella tendon) to return for Sunday's game against Milwaukee. Rivers said Delonte West (sprained right ankle) was doubtful to play against the Bucks. Rivers won't rush any of the injured Celtics. "We want the 1 seed, but we want health, too," he said. … 76ers director of statistical information Harvey Pollack, the NBA's only original active employee, received an autographed basketball from Ray Allen. He said "pass on what you know" when Pollack told him he was an original employee.