The 11th-seeded Buffaloes, who lost 13 of 16 conference games, threatened to avenge a 34-point regular-season loss before Baylor managed to put them away. Jordan Madden hit a 3-pointer with 39 seconds left to give the Bears (23-8) a six-point lead.
Brittany Spears had 24 points and Alyssa Fressle added 16 for Colorado (13-17), which was held without a field goal for the last 6:25.
The Bears advance to a quarterfinal Friday night against 12th-ranked Oklahoma. The game will mark the return of suspended star freshman Brittney Griner.
The Buffs finished with losses in 12 of their last 13 games.
Zachariason, averaging five minutes and 1.4 points, made a career-high five 3-pointers. She came in with a total of three 3-pointers in her 18 games.
Zachariason gave the Bears the spark they needed with Griner serving the second game of a two-game suspension for punching and breaking the nose of Texas Tech's Jordan Barncastle last week. The Bears also were without second-leading scorer Melissa Jones, who has battled injury the second half of the season.
Baylor won the regular-season meeting with Colorado 76-42 in Waco, Texas. Griner had 24 points, 10 rebounds and 11 blocked shots in that game.
Baylor lost 70-54 to Texas without Griner and Jones on Sunday, and looked headed for another defeat against the Buffaloes. Colorado led 62-58 when Chucky Jeffery scored with 6:25 left.
The Buffs didn't make another field goal against the nation's No. 2 team field-goal defense, but Baylor didn't have the game put away until Madden's deep 3-pointer with 39 seconds left.
The Bears wouldn't have been as close if it hadn't been for Zachariason's breakout night. She hit three shots from long distance in the first half.
The Buffs outscored Baylor 18-4 over the last 6:37 of the half. Spears's 3-pointer capped the run, which turned Colorado's 27-21 deficit into an eight-point lead.