Demajeo Wiggins added 10 points for the Falcons (8-4), who took control in the second half.
Bowling Green, which led 27-25 at the break, had an eight point surge to go up 41-34 on Rasheed Worrell's layup at the 11-minute mark. They stretched that to a 19-4 run for a comfortable 52-38 lead against the struggling Vikings.
All nine players scored for the Falcons, who shot 44 percent and made 15 of 18 free throws.
Cleveland State (4-8) only made two baskets in the second half until making two more in the closing minute. The Vikings shot 27 percent for the game (16 of 59), making just 3 of 20 3-pointers. Andre Yates had 11 points.