Shaw, who missed part of last week's game after aggravating a injury to his throwing shoulder, showed few signs of trouble Saturday, amassing 249 yards and two touchdowns for the Gamecocks (4-0, 2-0 SEC).
Marcus Lattimore, meanwhile, became South Carolina's all-time leader in rushing touchdowns with 31 after gaining 85 yards on 21 carries with two scores.
The victory was the Gamecock's eighth straight dating back to last season.
James Franklin was held to 92 passing yards on 11-of-18 efficiency for the Tigers (2-2, 0-2).
Swim Week Miami Beach 2014 [PHOTOS]