Turner finished with 10 points, including his layup that put the Sixers up 76-75. He added two free throws with 12 seconds to go.
Jrue Holiday scored 18 points and Andre Iguodala added 13 points, seven assists and six rebounds for the Sixers.
Kevin Garnett had 15 points and 12 rebounds and Ray Allen scored 17 points for the Celtics.
Game 3 is Wednesday in Philadelphia.
Philadelphia won its first playoff game in Boston since 1982 despite committing a playoff-high 19 turnovers and getting outrebounded 47-36.
THUNDER 119, LAKERS 90
OKLAHOMA CITY (AP) — Russell Westbrook had 27 points and nine assists and Kevin Durant added 25 points as Oklahoma City blasted weary Los Angeles in the opening game of the Western Conference semifinals.
The Thunder took a 15-point halftime lead, then opened the third quarter with a 15-2 blitz.
Oklahoma City led by as many as 35 points, getting a measure of vengeance for the elbow Metta World Peace delivered to the head of the Thunder's James Harden three weeks earlier.
Thunder starting centre Kendrick Perkins limped off after aggravating a hip injury from the first round.
Kobe Bryant and Andrew Bynum scored 20 points each for the Lakers and Bynum had 14 rebounds.
The Thunder committed a franchise-record four turnovers.
Game 2 is Wednesday night in Oklahoma City.
While the Lakers were making a quick turnaround less than 48 hours after ending the first round, the Thunder had eight full days off following their first-round sweep of defending NBA champion Dallas.