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.
"We started the game well, hitting 3-pointers to start and then kept getting good looks, but then we started to turn the ball over in the second half, and they came back," Washington State coach Ken Bone said.
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.
"We really needed that shot from Brock; they were coming back, and that 3 was huge. It stopped their momentum," Bone said. "Utah plays great defense, (and) I was glad we were able to keep up our shooting percentage."
Washington State shot 50 percent (24 of 48) from the field and 55 percent (11 for 20) from behind the arc.
"They (Washington State) had not been shooting well, but when they came out tonight and hit 3s at will, it was just their night," Utah coach Larry Krystkowiak said. "They made shots and we turned the ball over, and that was the game."
Washington State scored 28 points off 17 Utah turnovers.
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.