Ricardo Ratliffe scored 27 points, Phil Pressey 88, on Saturday.
Marcus Denmon added 15 points, including the free throw with 4.5 seconds left that counted as the difference as Missouri (18-1, 5-1 Big 12) won its fourth straight game since losing to Kansas State two weeks ago.
Quincy Miller poured in 29 points to lead Baylor (17-2, 4-2) and Pierre Jackson had 20. The Bears began the week undefeated at 17-0, the best start in program history, before losing to Kansas on Monday.
Brady Heslip's three-pointer at the buzzer made it a one-point final score, but Denmon had all but sealed the win by going 1-for-2 from the line at the other end.