BYU (12-4, 2-1 West Coast Conference) opened the game with a 12-1 run and Santa Clara (6-8, 1-2) never got closer than eight from there.
Jared Brownridge hit a 3-pointer to pull Santa Clara within 14-6 with 14:38 left in the half, but BYU scored 22 of the next 24 to open up a 28-point lead about 7 minutes later.
The Cougars turned 12 Santa Clara turnovers into 20 points and held a 45-28 rebounding edge.
Santa Clara made just 17 of 56 (30 percent) field goals, including 6 of 23 from 3-point range, and 6 of 15 free throws.
Haws moved past Devin Durrant into fourth on BYU's career scoring list with 2,289 points.
Brandon Clark led Santa Clara with 12 points.