The Flyers had held a comfortable lead for most of the game, and led 75-65 with 1:42 left as the UD Arena crowd started to pack up.
But before the fans could leave, Ole Miss guard LaDarius White nailed a dunk and 3-pointer to narrow Dayton's lead to three, 77-74, with 15.5 seconds left. The Flyers quickly huddled.
''(We said,) `Calm down,' " Jordan Sibert, who led Dayton with 20 points, said. ''Keep our confidence, don't lose faith and make our free throws.''
Ole Miss (8-4) fouled the Flyers' Dyshawn Pierre on the next play and he made one of two free throws to help Dayton escape with a 78-74 win.
Dayton coach Archie Miller called the game one of his team's more impressive non-conference wins, but wasn't surprised by the outcome.
''We have some hardheaded, tough kids,'' Miller said. ''There are some guys in there who really have been in some major-league battles in games, and they aren't going to run for cover if something happens.''
The Flyers entered Tuesday's game with an 11-game home win streak, dating to last season, and their hometown confidence was obvious for most of the game.
Kyle Davis put the Flyers up by 11 with back-to-back three-pointers with nine minutes left in the first half. On the next play, Ole Miss guard Stefan Moody tripped and lost possession. Sibert grabbed the ball, ran the length of the court and dunked it uncontested, nodding to the roaring crowd. The play capped a 15-3 first-half run and gave Dayton a 26-13 lead.
The Flyers relied on strong shooting and quick passes that left the Rebels defense a step behind. Dayton led by as much as 16 in the first half as the Rebels committed eight turnovers. The Flyers led 41-32 at the break and shot 6-of-9 from long range in the first half.
''Especially in our last three games, our defense has allowed the crowd to get into it, and the threes have started to drop,'' Dayton coach Archie Miller said. ''It's one thing to go 40 percent (from long), but it's another to bag six of them in the first half and give yourself the chance to go into halftime with a lead.''
Ole Miss pulled within seven points early in the second half and within six with nine minutes left, but every time the Rebels threatened, Dayton answered - including in the final minute.
Ole Miss: Ole Miss, who led the nation in free throw percentage entering Tuesday's game (78.3 percent), did not attempt a free throw in the first half. The Rebels shot 10 of 12 from the free throw line after halftime.
Jarvis Summers, who missed the Rebels' last game against Southeast Missouri because of back spasms, returned to peak form with a team-high 20 points. In Ole Miss' previous three losses this season, Summers had scored just eight points.
Entering Tuesday's game, Dayton had allowed just 55.3 points per home game. Ole Miss' 74 points were the most the Flyers allowed in a win this season.
Dayton hosts Duquesne on Saturday.
Ole Miss hosts Austin Peay on Saturday.