The 76ers rebounded the ball after Kris Humphries missed a jumper with 12 seconds left. They hurried up court and Turner released his shot just in time to give the 76ers only their third win in 13 games.
The Celtics lost for the 19th time in 22 games and dropped behind the 76ers in the standings by one game.
Spencer Hawes led Philadelphia with 20 points and tied his career high with four 3-pointers. Turner had 16 points and eight assists and Thaddeus Young added 16 points.
Jared Sullinger led Boston with 24 points and 17 rebounds and Jeff Green had 18 points, but just five after the first quarter.
Sullinger had broken a 90-90 tie with two free throws, putting Boston ahead with 3:06 left. Then both teams had trouble connecting from the line.
Michael Carter-Williams missed one of two for the 76ers, Jerryd Bayless missed two for the Celtics and Young also missed two. Carter-Williams missed another one before sinking his second, tying the game at 92 with 1:01 remaining.
Humphries put Boston back on top when he tipped in Sullinger's missed layup.
Philadelphia's free throw troubles seemed to end when Turner made one, cutting Boston's lead to 94-93. But he missed the second and Bayless rebounded. That possession ended when Humphries missed his jumper, setting up the 76ers for the winning shot.
Trailing 74-71 after the third quarter, the Celtics opened the fourth with a 15-4 run that gave them an 86-78 lead four minutes into the period. They hit three 3-pointers during the surge, two by Chris Johnson and one by Green.
But the 76ers responded with a 12-4 spurt and tied the game at 90, capping it with back-to-back dunks by James Anderson and Young.
Boston led 26-23 after the first quarter, but Philadelphia scored the first 10 points of the second to take a seven-point lead. Hawes began the surge with consecutive 3-pointers before Dewayne Dedmon made a layup and a dunk.
An eight-point run gave the 76ers a 48-34 lead, but the Celtics cut that to 53-47 at halftime.
NOTES: The 76ers made 14 of 25 free throws two nights after hitting 25 of 26 in a 124-113 loss to the Phoenix Suns. ... Boston G Rajon Rondo sat out the game after playing Tuesday night in a 114-88 loss to the New York Knicks. The Celtics are winless in the six games Rondo played since returning from a torn ACL that cut short his 2012-13 season. ...Their other starting guard, Avery Bradley, missed his fifth game with a sprained right ankle, but coach Brad Stevens said he's "very close" to returning. ... The 76ers began the night allowing an NBA-worst 109.9 points per game.