Jason Washburn scored 13 points and collected 11 rebounds, while Jeremy Olsen added 12 points off the bench, as the Utes held off a late Colorado rally to beat the Buffaloes, 58-55.
Utah won its first Pac-12 home game of the season and improved to 10-11 on the year, 2-7 in the conference.
Spencer Dinwiddie had 18 points, while Andre Roberson chipped in 10 points and 12 rebounds, for the Buffaloes (14-7, 4-5) who added a damaging loss to their NCAA tournament resume.
After trailing by as many as 22 points, Colorado made a late second-half run to get back into the game. The Buffaloes held Utah without a field goal over the final 10:44 of the game to whittle the Utes' lead down.
"I feel very happy for our kids in the locker room," head coach Larry Krystkowiak said. "They've been busting their tails and haven't got a break in a while. With the Coach Majerus tribute today, I think he was in the building for us going down the stretch."
At halftime, Utah honored their late coach Rick Majerus, who died December 1st from heart problems, by retiring his famous white sweater into the rafters at the Huntsman Center.
Several former Utah players were there, including all-time leading scorer Keith Van Horn and Denver Nuggets point guard Andre Miller.
"He was a tremendous figure in my life, especially after losing my father as a freshman" Van Horn said.
"He was probably the most intense coach I've ever been around," said Miller. "It was more than basketball. He gave me the opportunity to get an education and grow up and turn into a man. He left us too soon, but his time here was well spent."
The Utes next play at Oregon State Wednesday night.