Davis' free throws gave UMass (11-9, 4-3 Atlantic 10) a 66-61 lead and Dayton's Darrell Davis hit a 3-pointer with 3.9 seconds left. Play was stopped for a few minutes after Trey Davis blasted head-first into a screen at midcourt and needed to be helped off the court.
Donte Clark then missed the front end of a 1-and-1 for UMass with 2.1 seconds left and Jabarie Hinds sealed the win, blocking Kendall Pollard's desperation heave.
Jordan Sibert had 19 points and Pollard added 12 for Dayton (16-4, 6-2), which twice had the ball down by three in the final two minutes.
The Flyers closed within 46-45 with 15 minutes left before the Minutemen pulled away with an 11-3 run over the next eight minutes.