Gragg picked up 127 yards, while Tyler Wilson completed 16-of-20 passes for 248 yards and two scores as the Razorbacks (1-0) won in their first game under new Coach John L. Smith.
Smith replaced Bobby Petrino, who was fired in April following a scandal involving a female athletic department employee.
Knile Davis compiled 69 rushing yards on 15 carries in his first game back after missing the entire 2011 season with a broken ankle.
The Gamecocks (0-1) were led by Marques Ivory, who completed 14-of-26 passes for 160 yards and two touchdowns.
Alan Bonner compiled 107 yards and a touchdown on eight receptions for Jacksonville State.