Bogut, a seven-footer from Australia who leads the country with 17 double-doubles, added nine rebounds.
Bryant Markson added 15 points for the Utes, who extended the second longest winning streak in the nation to 18.
The Utes (23-3, 11-0 Mountain West Conference) clinched the league title with the victory.
Jacob Burtschi and Nick Welch led the Falcons (15-10, 6-4) with 15 points each. Air Force had its 24-game home winning streak stopped while losing for the first time at home this season (10-1).