There were three 3-pointers in the last 39 seconds of the game.
Matthew Wright, who made consecutive threes earlier in the second half to give the Bonnies the lead, knocked down another one from the right corner to give them a 68-65 advantage with 38.2 seconds left.
Dwayne Evans responded with a three to tie the score for Saint Louis with 20.9 ticks left, but he couldn't get out on Gathers quick enough after the Bonnies' guard got loose on a screen to take Charlon Kloof's pass at the point.
St. Bonaventure (18-14) will face the winner of Friday's Saint Joseph's-Dayton game in the semifinals on Saturday. The ninth-seeded Bonnies opened the tournament with an 82-72 win over La Salle on Thursday to stop a four-game losing streak.
Wright and Kloof scored 22 points apiece in the win and Youssou Ndoye had 13.
Mike McCall Jr. led Saint Louis (26-6) with 21 points and Evans scored 15.