Jack Cook scored on a 1-yard run, his second touchdown run of the game, with 51 seconds left. Then Zach Rumpke returned an interception 60 yards for a touchdown with 10 seconds remaining.
Pappas, who threw two touchdown passes in the first half, threw three more in the second half. His fifth touchdown pass of the game gave Morehead State a 38-28 lead with 7:23 to play.
Dayton rallied again, scoring on a 4-yard pass from Cook to Andrew Holderer with 2:55 to play and then tying the game on a 30-yard field goal by Sam Webster with 1:06 left.
Pappas completed 32 of 43 passes for 481 yards. Cook completed 23 of 39 passes for 428 yards.
Dayton’s Joe Swanson caught four passes for 151 yards and scored one touchdown.
Dayton returns to action at Drake (2-3, 1-1) at 1 p.m. next Saturday. Drake ended a three-game losing streak by winning 6-3 at Butler on Saturday.