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) lost their fourth straight bowl game, failing to capitalize on 100-yard rushing games from both Melvin Gordon and James White, and struggling after quarterback Joel Stave left in the third quarter with a shoulder injury.
Backup Curt Phillips was intercepted twice.
While the Gamecocks struggled to contain the Badgers rushing attack for most of the game, Shaw and Ellington did plenty to keep South Carolina productive on offense.
Trailing 17-13 in the third quarter, Ellington reeled in a juggling reception near the sideline on a fourth-and-7 play. Then, two plays later Shaw found Ellington for 22-yard touchdown strike to put the Gamecocks up by three.
The Badgers lost Stave on the next series, and with Phillips taking over, were stopped short on fourth down run inside the Gamecocks 30.
South Carolina took advantage, and needed just six plays for Shaw to find Jerrell Adams for a 3-yard touchdown that made it 27-17 with 11:05 to play in the game.