David Wear and Lazeric Jones added 15 points each for the Bruins (13-10, 6-5 Pac-12).
Brock Motum scored 19 of his game-high 25 points in the first half for the Cougars (12-11, 4-7). Reggie Moore added 12, Abe Lodwick 11 and Mike Ladd 10.
The Bruins were down 34-29 at the half but went into a zone in the second half that shut down the Cougars.
With 11:40 left, Washington State led 49-45. But it scored only one basket in nearly 9 minutes. During that span, the Bruins had a 13-2 edge and took a 58-51 lead with 4:49 left.
Lodwick broke the run when he hit a 3-pointer, but the Bruins closed out the game at the free throw line, hitting 6 of 8 in the final 30 seconds.