Bardo's 28-yard connection with Ross Smith early in the second quarter was the game-winner for the Flyers (7-3, 5-2 Pioneer League).
However the Bulldogs (4-7, 2-6) rallied quickly behind Malcom Weaver. Weaver and Derek O'Connor combined on a 62-yard touchdown with 8 seconds left in the first quarter and then Weaver scored on a 37-yard run at 8:50 of the second.
Connor Kacsor had 27 carries for 125 yards for Dayton.
O'Connor finished with eight catches for 144 yards as Butler's season came to an end.