Branden Dawson added 10 points for the Spartans (10-2), who struggled to put away the Falcons until late in the second half in a rare road game against a Mid-American Conference school.
Michigan State held Bowling Green (5-5) to just two points over a six-minute stretch in the second half to take control.
The Spartans went on a 14-2 run highlighted by Dawson's dunk after a steal, drawing a big cheer from the many Michigan State fans filling the Bowling Green arena.
Chauncey Orr led Bowling Green with 16 points.
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