The Gamecocks (46-18) will have to beat Kent State on Wednesday to keep alive their hopes of winning a third straight national title.
The Razorbacks (46-20) earned two days off and need one more win to go to the best-of-three finals.
Matt Vinson's RBI single in the fourth inning gave Arkansas a 2-0 lead. Evan Marzilli's two-out triple pulled the Gamecocks within a run in the fifth, but they got just one hit the rest of the way.
Stanek (8-4) allowed three hits and turned the game over in the seventh inning to Astin, who earned his 11th save.
South Carolina's Colby Holmes (7-2) allowed two runs on four hits in 3 2-3 innings. Tyler Webb shut down Arkansas on two hits over a season-high 5 1-3 innings, but his teammates couldn't get much going against the hottest pitching staff in the nation.
Arkansas pitchers have allowed just two runs over their last 32 1-3 innings. The Hogs have an ERA of 1.75 in eight NCAA tournament games.
The Razorbacks have won their first two games at the CWS for the first time since their initial appearance in Omaha in 1979. They've been here six times since.
South Carolina came from behind to win 11 times during the 22-game streak that started at the 2010 CWS.
The Gamecocks won two out of three against Arkansas during the regular season, but Stanek and Astin were too much for them to overcome Monday.
The Hogs had only six hits after banging out 10 in an 8-1 win over Kent State on Saturday.
They opened the scoring in the first on Dominic Ficociello's double. Their winning run came home in the fourth. Holmes walked Brian Anderson leading off, and he scored on a single by Vinson, who was hitting .209 out of the No. 8 hole.
South Carolina went three up, three down three of the last four innings.