Davis carried 26 times for 167 yards and scored all three of his TDs in the second half, in which the Gamecocks (3-1) overcame a 10-0 halftime deficit.
Davis scored twice from 13-yards out and once from 53 yards. His final TD of the day, from 13 yards with 10:31 to play in the fourth quarter, proved to be the game winner.
Dylan Thompson took over at quarterback for South Carolina when Connor Shaw sprained his shoulder on his first drive of the game. Thompson responded by running for a touchdown and completing 15-of-32 passes for 261 yards.
Central Florida (3-1) made its bid for an upset with a 1-yard touchdown run by Storm Johnson and a Shawn Moffitt field goal in the first half. Ranell Hall caught a pair of TD passes -- one for 73 yards -- from Blake Bortles in the fourth quarter.
Bortles threw for 358 yards and was picked off twice.