The Flyers (9-3) outscored Murray State 41-27 in the second half to snap a nation's-best streak of 16 consecutive wins for the Racers (9-2) on opponents' home courts. Their only other defeat this season came against Colorado in Charleston, S.C.
Dillard, whose status had been doubt after he suffered back spasms in Dayton's loss to Illinois State on Wednesday, logged a team-high 37 minutes and scored 13 of Dayton's final 20 points.
A layup by Dillard gave Dayton a 59-57 lead with 6:17 left. Dexter Fields answered with a 3-pointer to give Murray State its final lead, but Khari Price's 3-pointer put the Flyers back on top to stay.
Matt Derenbecker added 14 for Dayton.