Trasolini was 9 of 13 from the field. Brandon Clark came off the bench to score 14 points, and Kevin Foster added 12. Evan Roquemore had seven assists.
Santa Clara led 31-26 at halftime. The Broncos shot 38.7 percent from the field for the game, while Alcorn State shot 30 percent.
Marquiz Baker had 23 points for Alcorn State (2-10). Anthony Nieves and LeAntwan Luckett had 11 points apiece. Ian Francis had 11 rebounds.
Santa Clara (10-2) will play Wagner on Saturday in the title game of the classic. Alcorn State will play SMU.