The Gamecocks' senior was named the game's MVP after picking apart the Badgers defense, completing 22 of 25 passes for 312 yards. Shaw also had rushing and receiving scores.
South Carolina (11-2) won its third straight bowl game to cap its third straight 11-win season.
Bruce Ellington caught six passes for 140 yards and two touchdowns.
The Badgers (9-4) couldn't capitalize on 100-yard rushing games from both Melvin Gordon and James White, struggling after quarterback Joel Stave left in the third quarter with a shoulder injury.
Backup Curt Phillips was intercepted twice.
Wisconsin has lost four straight bowl games.
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