The Buffaloes (3-0) advance to Sunday night's championship game. They also earned a measure of payback for last March, when the Bears (3-1) knocked them out in the NCAA tournament's third round.
It wasn't easy for Colorado, though, which went 4 of 18 from the foul line. Andre Roberson missed two free throws with 3.1 seconds left that gave Baylor one final chance.
But Isaiah Austin's catch-and-shoot attempt was off the right rim as the buzzer sounded.
Baylor star Pierre Jackson had just 12 points after scoring 31 in an opening-round win here against Boston College.