Devin Oliver had 10 points and 12 rebounds for the Flyers (4-1), his first double-double.
After trailing 33-28 at the half, Andujar gave the Jaspers a 47-46 lead on a 3-pointer with 7:26 to go, and Beamon's jumper extended it to 51-48 at 5:55.
Dillard's 3-pointer at the 4:23 mark -- he scored seven points down the stretch -- put the Flyers ahead 54-51 at 4:23, and Dayton hit 8 of 10 free throws to seal it.
Manhattan trailed by as many as 11 in the first half but closed 28-27 on Donovan Kates' 3-pointer. Dillard's 3-pointer gave Dayton the 33-28 advantage at the break.