The Gamecocks (10-5, 2-2 Southeastern Conference) trailed by one when Brandon Wallace drove the lane for a dunk to give South Carolina the lead for good at 62-61 with 3:08 left.
After the shot clock ran out on the Volunteers (9-7, 2-2), Powell scored inside and was fouled by his former high school teammate, Major Wingate. He missed the free throw, but South Carolina led 64-61 with 1:56 left.
With the shot clock winding down, Andre Patterson drove the baseline for a reverse layup to pull Tennessee within 64-63 with 1:19 to go. But Tre Kelley hit two free throws - his first points of the game - to give the Gamecocks a three-point lead with 20 seconds to go.
Tennessee's freshman Chris Lofton, who leads the nation in 3-point shooting at 53.5 percent, missed a 3-pointer as time expired.
The Gamecocks shot 52.4 percent from the field, while the Volunteers hit 45.3 percent.
South Carolina out shot the Volunteers 54.2 percent to 40.7 percent but only led 32-30 after a first half, which had six lead changes, three ties and neither team leading by more than four points.
Scooter McFadgon, who scored 10 of his 17 points in the first half, scored on a three-point play to give the Volunteers their biggest lead at 53-47 with 10:34 remaining. But Tarence Kinsey, who had 12 points, answered with a 3 to keep South Carolina close.
The Gamecocks used a 9-1 run to go up 59-56 on one of two foul shots by Powell with 5:16 left. But C.J. Watson's 3-pointer pushed the Volunteers ahead again at 61-60 with 4:02 to go.
South Carolina Edges Past Tennessee, 66-63
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