The Wolverines (10-2) were playing their last game before Big Ten action starts next week but were unable to blow out the private Rhode Island school of 3,400 students.
Vlad Kondratyev had 20 points to beat the Bulldogs (1-10), whose only win this season is against Iona.
Michigan tied a school record with 16 3s, matching the mark set against Eastern Michigan in 2008.
Both teams hit over 50 percent of their 3-point attempts in the first half, but Michigan forced six turnovers while only committing one as it built a 45-35 lead.
Both teams continued to make outside shots in the second half. The Wolverines, though, got enough stops and took care of the ball, preventing Bryant from ever making a serious run.