The Utes had opened an eight-point halftime lead, 34-28, but Colorado State closed within five points, 42-37, with 16 minutes, 13 seconds to play on Micheal Morris' two free throws.
Utah used a 9-0 run over the next 2 minutes to lead by 14, and Colorado State would come no closer than seven the rest of the way.
"It was a hard-fought battle. Probably the difference was we made runs, and Andrew Bogut got put-backs. We'd make a run and get a stop, and he'd get a put-back. Those were back-breaking plays," said Rams'coach Dale Layer.
Bogut finished with 16 points and five of his 10 rebounds were on the offensive end. Teammate Tim Drisdom had a career-most 24 points to lead the Utes, while backcourt mate Nick Jacobson had 22 points.
Freshman guard Dwight Boatner led the Rams with 16 points - his career best. Morris added 15 and Ronnie Clark had 11. Forward Matt Williams had took game honors with a career-most 11 rebounds.
The Rams made only 23-of-59 field goals, 39 percent, the team's lowest mark from the floor in a home game this season, and 3-of-13 three-point goals.
"We had some good shots, but just couldn't get guys to make the shots," said Layer.
Colorado State returns to action Monday night, playing host to BYU on ESPN at 10 p.m.