Marquise Simmons hit 7-of-8 from the field for 15 points and Charlon Kloof had 14 points with six assists for the Bonnies (17-14), who got at least seven points from all seven players that took the floor.
Jerrell Wright netted a game-high 26 points and pulled down nine rebounds for La Salle (15-16), which advanced to the Sweet 16 last season before losing to eventual West Region champion Wichita State. Tyreek Duren donated 15 points with Steve Zack contributing 11 points and 11 boards.
Ndoye and Simmons combined to lead St. Bonaventure to a 10-3 lead early on. The Bonnies led throughout the half and took a 42-34 advantage into the locker room.
La Salle trailed 53-46 when a pair of Duren layups highlighted a 6-0 surge to get back within one near the midpoint of the second half. Jordan Gathers then hit two free throws as the Bonnies responded with a 5-0 spurt of their own.
Kloof's jam with just under two minutes to play made it 76-69, and St. Bonaventure got enough stops down the stretch to hang on.
St. Bonaventure will take on top-seeded Saint Louis in the quarterfinals.