Henry hit two free throws with 9.1 seconds left in regulation to give Ole Miss a 61-58 lead, but Tennessee's Skylar McBee banked in a 3-pointer with 2.1 seconds left to tie the game and send it into overtime.
The Rebels pushed ahead 70-63 in overtime on Murphy Holloway's putback, but Tennessee rallied to pull within 74-72 on two free throws by Jarnell Stokes. Henry closed out the game by making two free throws with 11 seconds remaining.
Ole Miss (20-12) advances to the tournament semifinals for the first time since 2007.
Both teams badly needed the win to improve mediocre NCAA tournament resumes, and the air of desperation was evident from the opening tip, with brutally physical play on both ends of the court. Points were at a premium and open looks were rare.
Ole Miss and Tennessee battled to a 28-28 halftime draw as the seventh-seeded Rebels managed to hang in the game despite rampant foul trouble. Five different players, including three starters, had two fouls, so coach Andy Kennedy was forced to use a patchwork of rarely used reserves like Aaron Jones and Maurice Aniefiok.
It worked decently, but the Rebels didn't have much answer for Golden, who scored 11 first-half points.
The second half was just as intense. Neither team led by more than four points.
Holloway was crucial down the stretch for the Rebels, scoring 14 points and grabbing 10 rebounds. Reginald Buckner had 12 points and eight rebounds. Ole Miss outscored Tennessee 38-12 in the paint.
Tennessee was the surprise of the SEC this season, recovering from some terrible losses during the nonconference portion of its schedule to finish 10-6 in the league and earn the No. 2 seed in the tournament.
The Volunteers have been getting NCAA attention because of the strong finish, but there's no doubt the loss to Mississippi hurts.
Ole Miss gets another chance to build its resume on Saturday in the semifinals against the winner of the Vanderbilt-Georgia game.