Paul Pierce hit a 3-pointer with 16.9 seconds left in OT to give the Nets the short-lived lead.
Turner, sensational all game, drove past a pair of defenders and tossed up the last-gasp shot. The ball bounced three times around the rim before it dropped through the net. After a brief review, the bucket stood, Turner was mobbed by his teammates and the Sixers snapped a seven-game losing streak.
Thaddeus Young scored 25 points for the Sixers, and Michael Carter-Williams had 15 points and 10 assists.
Alan Anderson had a season-high 26 points for the Nets, Pierce scored 24 with 10 rebounds, and Deron Williams had 17 points and 14 assists.
Brooklyn grabbed a 115-113 lead early in OT after Turner and Pierce swapped 3-pointers. Carter-Williams hit two free throws for a 116-115 lead, then had the assist to Young in front of Brooklyn's bench on a 3-pointer with 2:02 left.
The 76ers missed three shots on the same possession, setting up Pierce's clutch 3, Brooklyn's 15th of the game.
Turned out, the Sixers had one last dramatic shot of their own. Turner's 13th basket of the game was his biggest of the season, and he was mobbed on the court by a Sixers team buried well below .500.
Carter-Williams returned after a seven-game absence because of a skin infection and teamed with Tony Wroten in the backcourt for an effective 1-2 punch. Wroten scored 19 points. Thanks to OT, the Sixers finished with season highs in field goals (51) and assists (36).
Mirza Teletovic hit 6 3s and scored 18 points for the Nets. Brook Lopez had 22 points.
The Nets played without veterans Joe Johnson (personal reasons) and Kevin Garnett (rest).
Without their veterans, the Nets missed twice on one of the final possessions of regulation and the Sixers grabbed the rebound. Philadelphia rookie coach Brett Brown called timeout with 21.1 seconds left, setting up Carter-Williams' drive down the lane. He beat Williams to the basket, but ended with a wild misfire on a left-handed layup over Lopez.
Brooklyn grabbed the rebound and called timeout. Williams missed at the horn over Young's outstretched arm to send it into OT.
Neither team could break away in the fourth.
Young hit a mid-range jumper from the top of the key with 1:58 left for a 107-106 lead.
Anderson snatched it right back on two free throws - a lopsided edge for the Nets. The Nets made 21 of 30 free throws; the 76ers just 10 of 15.
Turner, who made his first eight shots from the floor, hit only the front end on a pair of attempts, but tied the game 108-all.
The Nets struggled to build a small lead for most of the quarter. They botched an alley-oop and Williams had the ball slip out of his hands on a layup attempt. Still, all five starters hit double-digit scoring in regulation, and Williams had a double-double.
Anderson, who averages only 8.0 points, connected on a pair of 3s during a 10-1 run late in the third that sent the Nets into the fourth with an 83-82 lead.
Johnson made 10 3-pointers, most in the NBA this season, and scored a season-high 37 points in the Nets' 130-94 victory over the Sixers on Monday night.
With Johnson out, Teletovic took over as Brooklyn's 3-point ace, hitting five in the first half against one of the worst-defending teams in the league. He nearly did as much damage alone from 3-point range as the Sixers did as a team.
NOTES: Wroten has started all games Carter-Williams has missed this season. ... There were 31 lead changes and 21 ties.