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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.