Shaw completed 22-of-25 passes for 312 yards and three touchdowns for the Gamecocks (11-2), who won their third straight bowl game. The senior quarterback added rushing and receiving scores.
Bruce Ellington threw a touchdown pass and caught six passes for 140 yards and two scores.
South Carolina defensive end Jadeveon Clowney said after the game that he will enter the 2014 NFL Draft. Clowney came into the season with sky-high expectations but fell short of immeasurable hype with a disappointing season. He had three sacks and 36 tackles heading into Wednesday's bowl game.
Joel Stave completed 9-of-13 passes for 80 yards, two touchdowns and an interception before leaving with a right shoulder injury for the Badgers (9-4), who lost in the Rose Bowl the previous three seasons. Curt Phillips connected on 7-of-12 passes for 37 yards and two interceptions.
Melvin Gordon carried the ball 25 times for 143 yards and James White rushed for 107 yards on 12 carries.
Ellington's 22-yard TD catch with 3:29 left in the third quarter gave South Carolina a 20-17 lead. Two plays before the score, Ellington caught a 22-yard pass on 4th-and-7.
The Gamecocks followed with a big stop on defense. Wisconsin moved the ball to the South Carolina 26-yard line, but Gordon was stopped for no gain needing just one yard on third and fourth down.
Shaq Roland caught passes of 12 and 49 yards on the ensuing South Carolina possession. Jerell Adams capped the quick series with a 3-yard TD catch, making it a 27-17 contest.
Kenzel Doe returned the following kickoff 91 yards for a score to get Wisconsin within three.
Shaw responded with a 1-yard TD run. Roland caught a 33-yard pass on the nine- play drive.
Phillips was intercepted twice in the final few minutes, sealing Wisconsin's fate.
Wisconsin tried a fake field goal on their first possession of the game. The holder, Drew Meyer, gathered the snap before throwing an incomplete pass.
The Badgers' next offensive series ended with Skai Moore picking off Stave. It took South Carolina just one play to capitalize, as Ellington caught a 39-yard TD pass from Shaw.
Wisconsin responded with a touchdown of its own. Gordon's 20-yard run and Jacob Pedersen's 36-yard catch moved the ball to the 1-yard line of the Gamecocks. Sam Arneson rumbled into the end zone to make it 7-7 with 12:45 left in the second quarter.
Ellington's 9-yard, double-reverse touchdown pass to Shaw put South Carolina back in front. The extra point was foiled by a bad snap.
The back-and-forth battle continued on the ensuing Wisconsin possession. The Badgers ran the ball 11 times on a 16-play drive that Jeff Duckworth capped with a 3-yard TD catch.
Jack Russell opened the second half with a 35-yard field goal, making it 17-13 Wisconsin.
Wednesday's game marked the first-ever meeting between the two teams on the football field ... Shaw carried the ball 16 times for 47 yards ... Roland caught six passes for 112 yards ... Shaw was named the game's MVP.