Conde opened the eighth with a double off Tyler Webb (5-1). He advanced to third on a groundout, and then scored when Yastrzemski dropped a bunt down the first-base line.
Will Clinard picked up the save by pitching two scoreless innings. Kevin Ziomek (5-6) got the win.
The Commodores (31-25) play Florida in Thursday's third round, while South Carolina (39-16) will take on Auburn.
Tanner English had a two-run single in the second to give the Gamecocks a 2-0 lead.
Conde made it 2-1 with a run-scoring sacrifice fly in the fifth. Spencer Navin tied the game in the sixth with a single that drove in Yastrzemski.