Chasson Randle added 16 points for the Cardinal (10-6, 1-2 Pac-12), who ended a two-game slide.
The largest lead for either team was six points until Stanford began pulling away in the final minutes.
D.J. Shelton hit consecutive 3-pointers for Washington State to tie the game at 37 with just under 13 minutes to play.
The lead changed hands six times afterward.
Stanford led 27-23 at halftime after Randle and Bright each hit a 3-pointer in the last five minutes.
This was the fifth game involving the Cougars that neither team scored more than 27 points in the first half.
It was a first for Stanford.
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DouDou Gueye, a 6-foot-10 center from Senegal, has signed with Ball State as a graduate transfer from South Carolina State.
Duke freshman point guard Derryck Thornton Jr. is transferring to USC, his father announced on Friday to Scout.com.
We have changes at the top of the draft and a shakeup in the lottery, with teams starting to make their final decisions. Get the latest in Chad Ford's Mock Draft 9.0.