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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.