Hunter Dickinson led the 11th-seeded Wolverines (18-14) with 21 points on 8 of 10 shooting from the field. Eli Brooks had 16 while Frankie Collins, pressed into action after DeVante' Jones was out with a concussion, had a season-high 14 to go along with six assists.
Dischon Thomas paced the sixth-seeded Rams with 15 points. Mountain West Player of the Year David Roddy was held to 13 to go along with six rebounds.
Colorado State ends their season at 25-7 after earning their highest seed in program history, having now lost six of their last seven NCAA Tournament games.
Story of the game
Colorado State jumped out to a big early lead, hitting four early three-pointers to take a 14-9 lead at the first media timeout. Nine turnovers in the first 12 and a half minutes by Michigan helped the Rams build a 28-13 advantage.
Collins was re-inserted into the game and sparked a turnaround. finishing six of seven from the floor. He scored seven straight points to trim the Wolverines deficit to 36-29 at halftime.
He picked up where he left off in the second half, capping a 6-0 run with a steal and dunk to further close the gap to 38-35 less than two minutes in.
Caleb Houston gave Michigan their first lead of the game when he nailed a three to make it 50-49 and another extended the advantage to four.
Colorado State hit a three-pointer to pull within one point, 53-52, but the Wolverines went on a 7-2 run punctuated by an and-one from Dickinson to take a 60-54 lead with just over six minutes remaining.
The big man continued to make the difference for the Wolverines in the final four minutes as he got a high-low pass from Moussa Diabate for an easy layup and converted on a pair of free throws two possessions later to give Michigan its biggest lead of the game at 66-58.
Colorado State looked to have an opportunity to get back in the game after a fast break layup and a subsequent offensive foul call that went against the Wolverines, but Michigan responded with a jumper by Brooks to make it 70-60, with 1:41 left to play.
Free throws were traded over the final few minutes as two by freshman Kobe Bufkin made it 74-63. Diabate added another to close out the game as Michigan outscored Colorado State 46-27 in the second half.