The Flyers (19-9, 7-6 Atlantic 10) trailed 58-52 with 4:33 left in the second half after Duquesne's Damian Saunders scored on a fastbreak layup. Dayton answered with 10 straight points, capped by Staten's free throw with 28 seconds left.
A 3-pointer by Duquesne's Sean Johnson cut the Flyers' lead to one. But the Dukes (17-8, 9-3) was unable to tie or pull ahead as Staten knocked down two free throws to give Dayton enough cushion.
Chris Johnson scored 14 points and had eight rebounds for the Flyers, who despite having 19 turnovers and shooting 36 percent (9 of 25) from the floor in the second half. Staten added 13 points.
Bill Clark led Duquesne with 17 points, Sean Johnson had 14 and Saunders added 13.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.