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 Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.