Down 46-43 midway through the second half, the Big Orange went on a game-winning 17-3 spurt to build a 60-49 lead heading into the final three minutes.
The win gives No. 20 Tennessee a 20-6 overall record and an 8-4 SEC mark. The Vols' Bruce Pearl has reached the 20-win plateau in 17 of his 18 seasons as a head coach and now stands 4-1 at Carolina's Colonial Center.
"You know, I'm starting to like this place a little bit," Pearl said on his post-game show. "This was four out of five."
Bobby Maze, who did much of the dandy defensive work on Downey, also led the Vols with 14 points.
"Bobby has got good length and good size for a point guard," Pearl noted. "When he keeps a guy in front of him like that and trusts his help, he does a pretty good job."
Wayne Chism, who scored a career-high 30 points in the Feb. 6 meeting, overcame some foul trouble to add 11 points and 9 rebounds.
Brandis Raley-Ross scored 16 points to pace Carolina, now 14-12 overall and 5-7 in league play. Downey added 15, just one above his season-low, and eight points off the 23 points-per-game average he brought into the game.
Tennessee's bench proved crucial. Vol reserves outscored Carolina's 20-3, and UT clearly was the fresher team in the game's final 10 minutes.
"Part of it is the commitment to the bench throughout the 40-minute period," Pearl said. "Kenny (Hall) played. Brian (Williams) played. Steven Pearl played. And they were out there at times when we were down significantly. You just hang in, knowing the game's played at the end, and I think that was a factor."
Tennessee played a sloppy first half, committing 11 turnovers en route to a 28-24 intermission deficit. Defense kept the Vols in the game, however, as they limited Downey to 1-of-8 shooting and Carolina as a team to 11-of-33 shooting (33.3 percent).
A 3-pointer by Maze put Tennessee up 34-33 early in the second half, then the lead seesawed back and forth until about nine minutes remained. That's when the Vols finally got their act together.
J.P. Prince opened the rally with a pair of free throws. Chism assisted Kenny Hall for a dunk, then hit two foul shots to put Tennessee on top 49-46. Prince added two more free throws as the Vols took a 51-46 lead with 7:14 remaining.
After a 3-pointer by Downey, Scotty Hopson hit a foul shot and Hall scored on a follow dunk. Prince added a steal and drive as the lead swelled to seven points (56-49) with 5:01 remaining.
Hopson, Prince, Maze and Hall hit a free throw each over the next two minutes, closing the 17-3 spurt and putting the game on ice.
Tennessee shot 48.8 percent (20 of 41) from the floor and 36.4 percent (4 of 11) from 3, while holding South Carolina to 31.7 percent (20 of 63) and 19.2 percent (5 of 26). The Vols dominated the backboards 40-30 and might have won handily if not for 19 turnovers.
"I'm not sure about the starting lineup; I'm not sure about the rotations," the coach said. "I don't think we started particularly well today, and that lineup of Melvin and Bobby out there together with J.P. at the 4, I don't see that as being something that's got a lot of legs to it."