After Odyssey Sims put the top-seeded Bears ahead 81-80 on a pair of foul shots with 9 seconds left remaining in the game, Baylor star Brittney Griner fouled Reid.
The Cardinals' senior forward proceeded to make the clutch free throws, securing the victory for Louisville (27-8).
Shoni Schimmel led the Cardinals with 22 points, including five 3-pointers, and Antonita Slaughter added 21 with six rebounds for Louisville, which will meet No. 2 Tennessee in the Oklahoma City Region final Tuesday.
Three-time All-American senior Griner was held to 14 points on 4-of-10 shooting for Baylor (34-2), which saw its 32-game winning streak snapped.
Sims led the Bears with 29 points, seven rebounds, five assists and six steals.