Quinnipiac (5-2, 1-0 Metro Atlantic Athletic Conference) trailed 34-25 in the first half but scored 16 straight points to take a 41-34 lead before halftime. Drame scored nine points during the run.
Fairfield (1-7, 0-1) was down 66-54 with less than nine minutes to play, but a KJ Rose layup with 4 seconds left brought the Stags within a bucket at 81-79.
Hearst then hit two free throws for Quinnipiac with 1 second left to make it a two-possession game and seal the victory.
Marcus Gilbert was 11-for-19 from the field and scored 31 points for Fairfield, which dropped its seventh straight game.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.