Santa Clara (3-0) also got 15 points from Evan Roquemore and 11 points each from Raymond Cowels III and Brandon Clark.
Cowels, Kevin Foster and Julian Clark each hit a pair of 3-pointers.
Upstate (1-3) was led by Torrey Craig's 17 points. Adrian Rodgers chipped in with 12 points and Ricardo Glenn grabbed 10 rebounds.
Roquemore had five assists and Trasolini blocked three shots.