Olivier Nkamhoua tied his career high with 27 points, including 13 straight for Tennessee during a decisive span in the second half for the fourth-seeded Volunteers, who advanced to the Sweet 16 for the first time since 2019.
Tennessee (25-10) ended Duke's 10-game winning streak and sent first-year coach Jon Scheyer, charged with replacing Mike Krzyzewski, home after just two NCAA tournament games.
"We're a tough, hard-nosed team," Nkamhoua said. "That's how we play everybody. But knowing they had a lot of freshmen, we knew that if we come in and apply more pressure and be tough and physical, then they would have to deal with it.
"What we were saying before the game is we were going to bring them into the mud with us and make them play a tough, hard-nosed game and see if they were ready for it."
The Vols used a brand of "bully ball" to send the fifth-seeded Blue Devils (27-9) packing.
"We feel we're at our best when we can do that," Tennessee coach Rick Barnes said.
Nkamhoua put an exclamation mark on Tennessee's victory with an emphatic slam with 1:15 remaining. It prompted Vols fans to start chanting and sent many Duke fans toward the exits.
"You have to really work for everything in a game like this," said Scheyer, whose team turned the ball over 15 times and made just 6 of 22 from 3-point range. "You have to work to get open."
Tennessee advanced to face Florida Atlantic or Fairleigh Dickinson on Thursday at Madison Square Garden in New York City.
Duke didn't handle Tennessee's physical style very well all afternoon, and the officials seemed content to let the Vols play their bruising style. The Volunteers set the tone early, clearly wanting to push around Kyle Filipowski and get hands in the faces of guards Jeremy Roach and Tyrese Proctor.
Vols big man Uros Plavsic picked up two offensive fouls in the first four minutes, both going against Filipowski. Duke's 7-footer later took an elbow to his face and ended up with a small cut under his left eye.
Proctor struggled to inbound the ball several times, getting a five-second call, turning it over once, and nearly giving it up again. Roach had even more issues, finishing the first half with three fouls and four turnovers.
WATCH: Duke players speak after loss
Duke players speak after loss
"We prepare for a dogfight every game," Nkamhoua said. "When we get people playing our game, it just guarantees that we're going to be in our element."
The Vols, meanwhile, took much better care of the ball than they did in their first-round victory against Louisiana-Lafayette. They turned it over just nine times, their fewest since point guard Zakai Zeigler sustained a season-ending knee injury last month.
Proctor led Duke with 16 points. Roach and Filipowski chipped in 13 apiece.
Dereck Lively II was scoreless but had 11 rebounds and two blocks.
"I thought we ran out of gas down the stretch," Scheyer said.
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The Associated Press contributed.