Josh Parker and Josh Benson scored 18 and 10 points, respectively for the Flyers (3-0), who outscored Ole Miss 13-6 in the extra frame. Dayton closed regulation play with a 14-2 run to tie the game at 65-65.
Ole Miss (2-1) had an opportunity to win in regulation, but Chris Warren missed a 3-pointer with 7 seconds left. The Flyers went on to dominate the overtime, hitting 9-of-10 free throws, capped with Johnson's layup at the buzzer.
Zach Graham led Ole Miss with 16 points, who led 46-33 at halftime. Nick Williams scored 14 points while Dundrecrous Nelson and Terrance Henry added 12 apiece for the Rebels.
The contest was a rematch of last year's NIT semifinals, won by eventual tournament champion Dayton 68-63.