Brock Motum added 17 points and DeAngelo Casto added 11 as Washington State (21-12) moved into the quarterfinals against Northwestern on Wednesday.
Oklahoma State (20-14) was led by Matt Pilgrim, who got a double-double with 17 points and 11 rebounds.
Thompson hit back-to-back 3-pointers in the first two minutes of the game to set the tone as Washington State started on a 9-0 run.
"I was open to start the game," Thompson said. "I just took that opportunity to shoot and made a few early."
The Cougars ended the first half leading 38-29, and went on a 12-6 run to start the second half. They took their biggest lead of the game, 51-37, with 13 minutes remaining.
"We started the game sluggish, and they got off to a fast start," Oklahoma State coach Travis Ford said. "We just couldn't get anything going in the first half."
Washington State kept the pressure on defense by playing zone and limited the Cowboys' inside play. The Cougars held the Cowboys' leading scorer, Marshall Moses, to a season-low two points and four rebounds.
"I thought we played better defensively in the second half and we shared the ball and that made a difference," Washington State coach Ken Bone said. "They did a nice job on Thompson, which gave Motum an opportunity to score."
Oklahoma State came in outrebounding their opponents by an average of 2.1 boards per game, but Washington State outrebounded the Cowboys 23-17 in the first half and finished the game with a 37-34 margin for the game.
Washington State will host Northwestern in the quarterfinal game Wednesday night in Pullman.