Marcus Johnson finished with 18 points for the Falcons (7-10, 2-3). Trey Thomas added 16 points for Bowling Green. Javontae Campbell finished with nine points and three steals.
Eastern Michigan went into the half leading Bowling Green 29-26. Henry scored 11 points in the half. Osojnik's 3-pointer with 11:05 remaining in the second half gave Eastern Michigan the lead for good at 45-44.
Both teams next play Tuesday. Eastern Michigan hosts Ohio and Bowling Green squares off against Miami (OH) on the road.
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The Associated Press created this story using technology provided by Data Skrive and data from Sportradar.