Brock Motum and Royce Woolridge added 14 points each and DaVonte Lacy and D.J Shelton 10 apiece for the Cougars (10-7, 1-3 Pac-12), who snapped a three-game losing streak.
Brandon Taylor had 13 points and Justin Seymour 11 for the Utes (8-9, 0-5).
Utah fought back from a 16-point deficit with the help of back-to-back three-point plays by Seymour to get within 47-41 with just under 10 minutes to play.
But Motum, who went scoreless in the first half, hit a 3-pointer from the top of the key and added a layup off a steal to help push the Cougars to a 60-46 advantage with six minutes remaining.
Utah got back within 10 on 3-pointer from Jarred DuBois with 3:46 left but got no closer. The Utes shot 46 percent (23 of 50) for the game.
Washington State scored 28 points off 17 Utah turnovers.