Fraser, who also had 10 rebounds and eight assists, put the Black Bears (8-11, 3-3 America East Conference) ahead to stay, 68-66, on a layup with 5:22 remaining.
The Catamounts (12-7, 5-2), who had won 11 of their past 12 meetings with Maine, scored just two points after tying the game 66-66 on Sandro Carissimo's 3-pointer with 5:45 left.
Edwards scored 15 points in the second half, when Maine rallied from a 41-36 halftime deficit.
Clancy Rugg scored 21 points to pace Vermont. The junior forward is averaging 18.8 points in four games since becoming a starter.
With game-time temperatures barely above zero, Maine held a "Beach Night" promotion, giving away cash and prizes to selected fans dressed in beachwear.
Sebastien Bellin's friend Chris Young joins Ryan Smith on Outside the Lines to discuss his friend's bravery, courage and strength after surviving the Brussels bombings in March.
Andrew White III is leaving the Nebraska men's basketball team and will play elsewhere for his final college season.
A cameraman fell down trying to film Ben Simmons at the NBA Draft. Flashing back to his LSU days proves this is nothing new.