Davis' plunge with 11:47 left in the game broke a 17-17 tie and wide receiver Pharoh Cooper later sealed the victory with a 26-yard scoring pass to Brandon Wilds.
South Carolina (10-2) forced six turnovers in the win, but nevertheless missed a chance to gain a spot in the SEC championship game when Missouri bested Texas A&M Saturday.
Connor Shaw completed 14-of-26 passes for 152 yards with a score and also ran for a touchdown, picking up 94 rushing yards on 22 carries.
Taj Boyd went 19-of-27 passing for 225 yards but was intercepted twice for the Tigers (10-2). He also gained 16 yards with a TD on 15 carries.
Roderick McDowell carried the ball 14 times for 111 yards and score.