Santa Clara (8-7, 1-1 West Coast Conference) scored 12 straight points to build a 52-37 lead with 13:17 left in the game.
Portland (8-6, 0-2) later answered with a 9-0 run to close the gap to 55-52 and Thomas van der Mars' three-point play kept them within 58-55. But Santa Clara answered with a 10-3 run and made eight free throws in the final 2 minutes.
The Broncos shot 12 of 23 from 3-point range and Roquemore was 5 of 7 from long distance. His back-to-back 3s in the first half gave Santa Clara the lead for good at 28-24.
Portland out-rebounded Santa Clara 43-27.