The 76ers ended a three-game skid and climbed past Boston out of the cellar in the Atlantic Division.
Philadelphia trailed by as many as eight points in the fourth quarter, but tied the game on a pair of free throws by Michael Carter-Williams with 1:01 to play.
A tip-in by Kris Humphries put Boston back in front with 43 seconds remaining and Turner was then fouled.
Turner could make only 1-of-2, which left the 76ers trailing by one. Humphries tried to give the Celtics a three-point cushion, but his jumper misfired with 12 seconds left.
That gave the 76ers to complete the rally and Turner made good on the opportunity. It was Boston's fourth loss in a row.
Jared Sullinger produced 24 points and 17 rebounds for the Celtics.