Faisal Aden scored 20 points for the Cougars (19-10, 9-8 Pac-10).
In the final 4:45, Washington State had one shot from the floor: a layup by Aden, after he stole the ball from Vucevic. The basket put the Cougars up 77-70 with 1:41 remaining.
The rest was done at the line, where Washington State went 10 of 14 in the final 4:45, and 8 of 8 in the final 3:03.
The Cougars lost guard Reggie Moore to a sprained ankle seven minutes into the game. He will be re-evaluated on Friday.
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Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.
Recruiting reporter Jeff Borzello has gotten grilled for his selections of underachieving and overachieving college basketball programs. He joins Phil Murphy to explain his rankings.