Chaz Williams scored eight points and was 1-of-7 from the field, but he hit the decisive free throws late in the game as the Minutemen (14-1, 2-0 A-10) rallied for the win.
Cady Lalanne scored 16 points for UMass and Williams contributed nine assists.
Charlon Kloof scored 15 to lead the Bonnies (11-5, 1-1) who shot 50 percent from the field but could not extend their four-game winning streak.
St. Bonaventure led 32-25 at halftime and led 68-64 with 2:18 to play but did score again and watched as UMass went on a 9-0 run to grab the victory.
2014: The Year in Music [PHOTOS]