Pierce, who finished with 25 points, made two free throws in the closing seconds after the 76ers had erased a 19-point deficit and pulled to within 104-102.
Shaun Livingston then stole the ball and sealed the victory with two more free throws as the Nets snapped a three-game losing streak.
Deron Williams provided 21 points, Mirza Teletovic added 20 and Livingston finished with 13, eight assists and seven steals for Brooklyn, which benefited from 25 Sixers turnovers.
Michael Carter-Williams led Philadelphia with 21 points.
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