Jon Mesghna added 13 points for Maine (5-8).
Ahead 48-44 with 17 minutes to play, Mesghna's 3-pointer and Edwards' layup gave Maine its biggest lead of the half, 53-44, with 16:22 remaining.
Quinnipiac (4-7) answered with a 15-6 run to tie the game at 59 with 9:48 left to play.
The teams traded baskets over the final 10 minutes but Edwards scored nine points during the span to give the Black Bears a 74-69 advantage with 1:17 remaining.
Evan Conti made a layup to cut Quinnipiac's deficit to three, 74-71 with 47 seconds left to play, but Zaid Heart missed a tying 3-pointer and Fraser hit two free throws for Maine with 5 seconds left to seal the victory.
Ike Azotam finished with 16 points and nine rebounds for Quinnipiac.