Hitchens hit four 3-pointers in the final 1:22 of regulation and during the overtime period, as the Dukes (7-4) erased a nine-point deficit.
Stetson (4-8) used a 15-0 run to take a 49-40 lead, but James Madison came back to force overtime on Hitchens' 3-pointer with 3.6 seconds remaining in regulation.
The Hatters tied the game at 69 on Adam Pegg's three-point play with 39.5 seconds remaining.
Aaron Graham led Stetson with a career-high 26 points, while Pegg finished with 19.
Moore had 10 points for James Madison, which lost 79-60 to Rhode Island on Thursday night. Hitchens was 10 of 21 from the field and 6 of 14 overall from behind the arc against the Hatters.