It was the first win in the SEC in the Holly Warlick era and it came at a tough venue as the Gamecocks had used stingy defense to hold 10 opponents to under 50 points.
The Lady Vols led by just one point at halftime, 32-31, and then lost the lead to open the second half. They went on a 12-0 run - aided by South Carolina missing 11 straight field goals, and put the game out of reach.
"It was a tale of two halves," Warlick said.
Harrison set two career highs - blocks with seven and boards with 14.
South Carolina was led by Tiffany Mitchell with 14 points, while Ashley Bruner had 12 and Ieasia Walker added 10.