Jehvon Clarke added 13 points, Richaun Holmes had 11 and Anthony Henderson chipped in 10 for the Falcons.
Bowling Green (18-8, 10-5 Mid-American) has now won five of the last seven and is tied with Kent State atop the Mid-American East after Miami (Ohio) upset Kent State 86-81 in overtime Tuesday.
Bowling Green had a 40-22 halftime advantage. The Bobcats opened the second period with a 15-8 run to close to 51-37. Parker nailed back-to-back treys to give Bowling Green a 62-39 advantage. The Bobcats charged back as Ryan Taylor dunked to start an 8-0 run to close to 70-60 with 2:49 left. David Joseph and Holmes closed it out with six straight free throws.
Maurice Daly Ndour had 23 points and Antonio Campbell added 14 with 12 boards for Ohio (9-17, 4-11).