The win sends the fourth-seeded Bonnies (20-11) to the NCAA tournament for the first times since 2000.
Nicholson wrapped up a solid performance in Atlantic City that totaled 70 points, 30 rebounds and 16 blocked shots in three games. He was the only Bonnies player to reach double figures Sunday although Da'Quon Cook and Charlon Kloof both scored nine points.
Tu Holloway led Xavier (21-12) with 17 points and Mark Lyons scored 16. Xavier was seeded third in the tournament.
St. Bonaventure led 37-24 at halftime.