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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.