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.