Saint Joseph's (13-8, 4-4) built a 43-36 lead in the second half. But the Hawks missed four of their next five shots as Dayton rallied to take its first lead of the frame, 47-45, on a Dillard 3-pointer with 5:02 remaining.
From there, teams exchanged the lead five times before Dillard sank a trey, followed by a jumper, to put the game away. Dillard scored the 14 of the Flyers' (13-9, 3-5) last 15 points.
The 6-foot guard hit four free throws in the final 30 seconds and improved to 30 for 30 from the charity stripe this season with less than 2 minutes left to play.
Carl Jones scored 12 points for Saint Joseph's, which hasn't defeated the Flyers since the 2000-01 season.