Shaw completed 21-of-29 passes and ran for a score for the Gamecocks (2-1, 1-0 SEC), who held off a late rally to secure the win.
Bruce Ellington made eight catches for 120 yards and a score while Nick Jones and Brandon Wilds each contributed a TD reception.
The Commodores (1-2, 0-1) got 147 passing yards and a TD throw from Austyn Carta-Samuels, who also rushed for a touchdown.
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