The Gamecocks (5-1, 2-1 SEC) won their 10th straight over Kentucky (2-3, 0-3).
Garcia had touchdown passes of 10, 28 and 22 yards to freshman Alshon Jeffery. Garcia added what proved to be the winning margin with his leap from the 1 with 8:22 remaining to give South Carolina a 28-20 lead.
Kentucky had a chance to tie after Randall Cobb's 2-yard TD run with 4:34 left. But Will Fidler's pass was knocked down by defensive end Cliff Matthews.
Facing third-and-4 moments later, Garcia gained 5 yards leaping over a Kentucky defender to keep South Carolina moving with 3:02 to go. Kentucky never got the ball back as South Carolina matched its best start in Spurrier's five seasons.