Stowers hit a three-run homer in the fourth inning and added a three-run triple during a five-run ninth for the fifth-seeded Cardinals (41-16).
Stowers' triple followed Logan Wyatt's run-scoring single for Louisville, which plays fourth-seeded Duke (39-14) on Friday with the winner advancing to the semifinals.
Reid Detmers (4-1) struck out five in 5 2-3 innings for Louisville.
Colin Peluse (6-2) allowed three runs and five hits in 4 2-3 innings for the ninth-seeded Demon Deacons (25-31).