The Redhawks beat Bowling Green at Oxford four straight times.
The Falcons (19-8, 11-5) came into the game as a co-leader of the Mid-American Conference East Division with Kent State. More importantly, the win keeps Bowling Green among the top four teams in conference, which would earn a first-round bye in the conference tournament.
Chris Bryant scored a layup with 2:23 left to give the Redhawks (12-17, 7-9) a 51-50 lead, but Denny answered with a 3-pointer to put Bowling Green ahead for good, 53-51 with just over two minutes left.
Denny finished with 17 points and Holmes added 15 while Bowling Green converted 19 of 23 attempts from the free throw line.
Eric Washington led Miami with 16 points.