Drummond hit four free throws for Toledo (8-0) in the game's final minute, including two with 25 seconds remaining to extend the Rockets' lead to 80-77.
Drummond committed a foul with 1 second remaining, sending Robert Morris to the free throw line trailing by three. Karvel Anderson missed the front-end of the one-and-one and Toledo held on for the win.
Robert Morris shot 73.9 percent (17-for-23) from the field in the first half but led just 41-37 at halftime. The Colonials shot 63.3 percent for the game. Lucky Jones scored 25 for Robert Morris and Anderson added 23.
Michigan has hired assistant basketball coaches Billy Donlon and Saddi Washington.
Duke and Cincinnati, 2016 NCAA tournament teams, highlight the eight-team field for the Naismith Memorial Basketball Hall of Fame Tip-Off Tournament.
NCAA champion Villanova will play Notre Dame and Pittsburgh will play Penn State in the inaugural Never Forget Tribute Classic at Prudential Center on Dec. 10.