The Bonnies shot only 36 percent from the field, but made 30-of-34 from the foul line to hand the Minutemen only their third loss of the season.
It was the first victory for St. Bonaventure over a ranked opponent in 14 years.
St. Bonaventure led by a single point with 8 minutes to play before ending the game on a 23-11 run.
Kloof scored 14 points and went 8-of-9 from the line. Dion Wright and Youssou Ndoye both added 12 points for the Bonnies (13-8, 3-4 Atlantic-10 Conference).
Massachusetts made three more field goals than did St. Bonaventure, but hit 22 fewer free throws. The Bonnies also dominated the backboards 41-29.
The Minutemen (17-3, 4-2 A-10) were led by Trey Davis with 18 points.