The Tigers, who trailed by as many as nine points, rallied from a 43-36 deficit in regulation to tie the game at 47-47 on a basket by Korvotney Barber, who was fouled on the play but missed the free throw.
Auburn had more five possessions, including the last one in regulation when Lucas Hargrove couldn't hit a three-pointer as the Tigers held the ball for the final 33 seconds.
Auburn's downfall was on the boards and at the free throw line. The Flyers out-rebounded the Tigers 60-43, with a 22-9 margin on the offensive glass, and the Tigers compounded the problem by making just 12-26 free throws. The Flyers hit 20-31 free throws.
Dayton scored the first points in overtime on a basket plus free throw by Chris Wright.
Reed, who had just one point at halftime and 21 after that, hit a three to tie the game at 52-52 with 1:40 to play.
Wright then put Dayton up for good. The Flyers led by four until Tay Waller hit a three with 16 seconds left to cut the gap to 56-55.
Marcus Johnson made two free throws for Dayton with 13 seconds to extend the lead back to three. Reed then hit both ends of a one-and-one with 11.5 seconds remaining.
Auburn wasn't able to get a steal and fouled Johnson with 4.7 seconds left. He hit two free throws to make the score 60-57.
Reed was fouled with 1.4 seconds. He made both ends of the one-and-one to cut the lead to one again, but Dayton threw the ball deep to run out the clock.
The loss drops Auburn to 3-2 while Dayton improved its record to 5-0.
Dayton managed to win despite shooting just 27.8 percent from the field including going 0-23 from three-point range. That made Auburn's 7-31 shooting from three-point range looked really good in comparison. The Tigers hit 20-58 field goals for 34.5 percent.
Waller and Barber scored 10 apiece for the Tigers while Johnson led the Flyers with 16 points and Wright scored 10.
The Tigers return to action at 4:30 p.m. on Saturday vs. Northern Iowa in the final game of the Chicago Invitational.
Auburn coach Jeff Lebo said, "Everything offensively was a struggle for us and Dayton is a very good defensive team. I was worried about how we were going to be able to score in this basketball game and my worries came true.
"We had some great opportunities and again shot the ball so poorly from the foul line, but our defense kept us in the game," he added.
"I liked our toughness when we got nine in the second half. We came back and had chance to win the game. We had some great looks in the last three minutes of the game."
The Tigers led only briefly in the game at 14-13 on a layup by Hargrove. Dayton took a 26-21 lead into the locker room and built a 30-21 margin early in the second half.
Commenting on his leading scorer's performance, Lebo said, "DeWayne Reed played a lot of minutes (42) in this game, and he is getting better and better and better. He is shooting the ball a little bit better for us, and he is a junior now and is getting more comfortable playing the point guard position. I thought he did a nice job in the second half in bringing us back."