Harris wrapped Allen with his arm during the final 12 seconds, impeding the center's freedom of movement and preventing him from rolling to the basket quicker after setting a screen.
Instead of scoring on the possession to tie the game at 110, Allen turned the ball over when three Sixers defenders swarmed him in the paint. Philly then locked up a 112-108 win and a commanding 3-1 series lead.
Nets head coach Kenny Atkinson complained about the non-call after the game.
"Judge for yourself if you watch the clip, but there was a clear wrap by Tobias Harris on the roll," Atkinson told reporters.
The series has become increasingly chippy. The NBA fined Jimmy Butler and Jared Dudley on Sunday after they were ejected following a fracas in the third quarter of Game 4. Also on Sunday, Nets general manager Sean Marks was suspended for one contest and fined for entering the referees' locker room after Game 4.
The 76ers can win the series with a Game 5 victory in Philadelphia on Tuesday.