Joey Pankake drove in two runs during a five-run second inning for the Gamecocks (43-19), who forced a decisive game Monday in the best-of-3 series with the winner going to the College World Series.
The Tar Heels (56-10) won Saturday's opener 6-5 on an RBI single in the ninth, putting them within a win of returning to Omaha, Neb., for the sixth time in eight seasons.
But the No. 1 overall seed in the NCAA tournament got a short outing from a starting pitcher and fell behind early for the second straight day.
It was North Carolina's first shutout loss all year and its four hits matched a season-low. Before Sunday, North Carolina's worst loss was a 10-4 home defeat to No. 6 national seed Virginia on May 16.
South Carolina is trying to get back to Omaha for the fourth straight year. The Gamecocks won the 2010 and 2011 national titles and finished second last year.
The Tar Heels started the year 39-2, won the Atlantic Coast Conference tournament title and haven't lost consecutive games all year. But they barely made it out of the NCAA regionals and have taxed their bullpen in the super regionals thanks to the ineffective performances of starters Kent Emanuel and Hobbs Johnson.
A day after Emanuel had his shortest outing of the season at 2 1-3 innings, Johnson (4-1) turned in the shortest outing of his career by managing just five outs before heading to the dugout in the second.
By then, Pankake had driven in a pair of runs on a double down the left-field line and L.B. Dantzler had followed with a two-run single to right. Then Tanner English - who also had three stolen bases and a diving catch in center field in the ninth - drove in another run on a bunt to make it 5-0.
Not that Montgomery needed much help on this day.
The sophomore left-hander didn't let a UNC base runner reach third all day. He threw 121 pitches and struck out three while walking just one, dominating a lineup that had produced the most runs in the nation (8.1 per game) entering the super regionals.
The starters for Monday's game are expected to be sophomore right-hander Benton Moss (8-1) for North Carolina and freshman left-hander Jack Wynkoop (7-3) for South Carolina.