The 76ers ended a seven-game losing streak.
Turner went to the basket as time was running down, but his layup attempt with 6.9 seconds remaining was blocked by Alan Anderson. The ball went out of bounds off Brooklyn and, after a time out, Turner drove inside again and lofted a shot over two defenders.
Turner also made 1-of-2 foul shots with 51 seconds left in the fourth quarter for the final point of regulation. He finished with 29 points, 10 rebounds and five assists.
Philadelphia has not won in regulation time since Nov. 8. Their only four victories since then have all come in overtime.
Thaddeus Young added 25 points for Philadelphia and Tony Wroten had 19.
Anderson led the Nets with 26 points and Paul Pierce had 24. The Brooklyn bench contributed only 13 points.