Levi Knutson added 12 points for the fifth-seeded Buffaloes (20-12), who moved on to face No. 4 seed Kansas State in the quarterfinals on Thursday.
Jake Anderson poured in 33 points for Iowa State (16-16) and Diante Garrett had 19.
The Cyclones took a 70-64 lead on Jamie Vanderbeken’s free throw with three minutes left, but Colorado closed with a 13-5 burst to win the game.
During the run, Burks completed a three-point play to tie the score and then hit a jumper to make it 74-72, giving the Buffaloes a lead they wouldn’t relinquish.
Not that Iowa State didn’t have chances down the stretch.
During one series, with the Cyclones trailing 75-72, Vanderbeken hit the front of the rim with a long three-point try several feet behind the arc. Iowa State kept possession, but Garrett’s pull-up jumper in the lane rattled in and out.
Andre Roberson and Higgins both made one free throw in the final 15.6 seconds as Colorado hung on.