The game-winning kick was set up when Justin Worley marched the Volunteers (4-3, 1-2 SEC) on a late drive in the closing minutes of the contest.
Tennessee took over at its own 35-yard line with 2:48 remaining while trailing by one point at the start of the decisive drive.
The key play came on 3rd-and-10 when Worley found Marquez North along the left sideline for a spectacular 39-yard catch to the Gamecocks' 26-yard line.
Marlin Lane added a 14-yard run to the 2-yard line with 27 seconds left.
After running down the clock, Palardy secured the upset with the game-winning boot.
South Carolina fell to 5-2 and 3-2 in the SEC with the surprise loss.