The Falcons (7-2) made 32 of 58 (55 percent) shots with 23 assists, including nine from Ismail Ali. Bowling Green made 10 of 18 3-pointers, including four by Denny.
Isiah Jones scored 12 points to lead the Redhawks (0-8), who made only 22 of 69 (32 percent) shots, and sank just 3 of 17 from 3-point range.
Bowling Green never trailed and was up 35-22 at halftime. The lead stayed in that range until a 13-4 run, including 11 points from Parker, made it 69-45 with 5:11 to go. The Falcons' biggest lead, 28 points, came with 1:31 to go.
The Falcons have their first six-game winning streak since 2008-09.