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.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.
College basketball fans should be excited about next season's Jimmy V Classic, an event that will feature Duke's heralded freshman class.