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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Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.
The dust has settled after players made their NBA draft decisions. Which college teams won? Which lost? Well, Villanova is pretty happy. USC, meanwhile, might not be as thrilled.
The 2017 recruiting class is short on point guards, with Trevon Duval leading only eight prospects from the ESPN 60 who are still available.