Charlie Enquist had 18 points and 10 rebounds for the Cougars (6-4).
Kevin Foster scored 16 points, Niyi Harrison 14 and Evan Roquefort 12 for the Broncos (5-3).
Washington State dominated inside, posting a 33-25 rebounding advantage and outscoring Santa Clara 44-22 in the paint.
The Cougars had runs of 9-2 and 8-0 in the final seven minutes of the first half to take a 48-27 lead into the break.
Washington State shot 67.4 percent (31 of 46) from the field, including 46.2 percent (6 of 13) from 3-point range.