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, who blew a 10-point lead in the fourth quarter as the Celtics won Game 1.
Kevin Garnett had 15 points and 12 rebounds and Ray Allen scored 17 points for the Celtics.
Game 3 is Wednesday in Philadelphia.
Brandon Bass had 12 points for the Celtics, who couldn’t quite repeat their comeback in the series opener.
Rajon Rondo and Ray Allen both missed shots that would have put Boston ahead, then Rondo fouled Turner with 14.4 seconds left as the shot clock was winding down.
The Celtics fouled Turner again with 12 seconds and he hit both free throws to extend the lead to 78-76.
Fans grew restless as the second half opened with sloppy, choppy play by both teams. Boston led 38-36 at halftime and nearly 7 minutes into the third quarter the score was just 43-41 with the Celtics still ahead. When the shots finally started falling, they were all for Philadelphia.