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 scores rushing and receiving. South Carolina (11-2) won its third straight bowl game to cap its third straight 11-win season.
After untimely injuries and losses culminated in the Gamecocks missing a spot in the BCS, Shaw said this performance offered some redemption.
"I told the team before the game that we've faced every possible scenario we could possible face this season and that Wisconsin would be no different," Shaw said. "I'm so glad the way we battled throughout the game and our defense came and played.
"I couldn't be more proud."
The game also turned out to be the final college contest for Jadeveon Clowney, who said afterward that he would forgo his senior season and enter the NFL draft.
"Before we even put the pads on, I thought we've only got 60 minutes and it's over with. I'm going to be sad about it. ... I'm excited to move forward with my life though."
Bruce Ellington caught six passes for 140 yards and two touchdowns. Shaw Roland also hauled in six catches for 112 yards.
"The guys, we came together as a team today and Connor did a great job of leading us," Ellington said. "We just came out and played."
Shaw's receivers caught balls in traffic and in the open field, gashing a Wisconsin defense that surrendered 438 yards for the game. The Badgers also allowed two fourth-down conversions, one which set up a 22-yard touchdown pass from Shaw to Ellington that put the Gamecocks up for good late in the third quarter.
Wisconsin (9-4) lost its 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 couldn't contain the Badgers' rushing attack for most of the game, Shaw and his receivers 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. Two plays later Shaw found Ellington for the 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 a 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.
"You kind of walk a fine line between being aggressive, getting after the quarterback and containing him," Badgers coach Gary Andersen said. "Our plan was to be aggressive. At times we didn't get the pressure we should have and at times he was able to extend plays."
Wisconsin wasn't done. Kenzel Doe took the ensuing kickoff and ran it back 91 yards for a score to get the Badgers back within a field goal.
But Shaw went back to work.
Pinned inside his own 15 to start the drive, he used a combination of runs and passes to set up his 1-yard touchdown plunge to cap a nine-play, 81-yard drive that made it 34-24.
Wisconsin appeared to be done after Phillips was intercepted by Kaiwan Lewis with less than five minutes to play, but the Gamecocks gave it right back on Brandon Wilds' fumble on the next series.
The Badgers picked up a few first downs, but then Phillips was intercepted again by Skai Moore with 3:14 left to end the threat.
"We were very good defensively in the fourth quarter. It was a fourth-quarter game," South Carolina coach Steve Spurrier said.
Clowney had four tackles in the first half, including one for a loss. But he was mostly a non-factor early as the Badgers alternated White and Gordon in the backfield.
Wisconsin rushed for 293 yards in the game, but had no rushing touchdowns. The badgers hadn't lost by double digits since October 2010 (also 34-24 to Michigan State). Since then, they'd lost 13 times, all by seven points or less.
Gamecocks' defensive end Victor Hampton, whose hit knocked Stave out of the game, confirmed afterward that he would skip his senior season and enter the NFL draft. He said he thought South Carolina's defense displayed its true personality when it had to.
"That was a knock-down, drag out fight," Hampton said. "Everybody was saying we couldn't stop the run, but we showed them different. They got some yards on us in the first half and (Melvin Gordon) was really impressive, but in the second half, it was all over. We shut them down."
No. 8 South Carolina 34, No. 19 Wisconsin 24
Wisconsin 0 14 3 7 24
South Carolina 7 6 7 14 34
SC • Ellington 39 pass from Shaw (Fry kick), :41.
Wis • Arneson 1 pass from Stave (Russell kick), 12:45.
SC • Shaw 9 pass from Ellington (run failed), 6:48.
Wis • Duckworth 3 pass from Stave (Russell kick), :13.
Wis • FG Russell 35, 11:19.
SC • Ellington 22 pass from Shaw (Fry kick), 3:29.
SC • Adams 3 pass from Shaw (Fry kick), 11:05.
Wis • Doe 91 kickoff return (Russell kick), 10:54.
SC • Shaw 1 run (Fry kick), 5:48.
Attendance • 56,629.
First downs 21 20
Rushes-yards 43-293 34-117
Passing 117 321
Comp-Att-Int 16-26-3 23-26-0
Return Yards 0 4
Punts-Avg. 0-0.0 3-33.7
Fumbles-Lost 1-1 2-2
Penalties-yards 2-15 4-23
Time of Possession 29:26 30:34
Rushing • Wisconsin, Gordon 25-143, White 12-107, Clement 1-32, D.Watt 1-8, Phillips 1-7, Stave 3-(minus 4). South Carolina, Davis 9-49, Shaw 16-47, Wilds 3-16, P.Cooper 2-9, Carson 1-0, Team 3-(minus 4).
Passing • Wisconsin, Stave 9-13-1-80, Phillips 7-12-2-37, Meyer 0-1-0-0. South Carolina, Shaw 22-25-0-312, Ellington 1-1-0-9.
Receiving • Wisconsin, Abbrederis 5-30, Pedersen 3-50, White 2-8, Duckworth 2-7, Wozniak 1-7, Erickson 1-6, Doe 1-3, Arneson 1-1, Gordon 0-5. South Carolina, Ellington 6-140, Roland 6-112, Jones 3-25, Adams 3-17, Davis 2-10, Shaw 1-9, Wilds 1-8, Jeffery 1-0.