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.
High school junior Zach Brown, a 7-footer from Miami, has rescinded his commitment to UConn, sources told ESPN.
Reserve center Akolda Manyang has been charged with felony aggravated assault after being accused of punching a man in the face without provocation.
Should the 76ers take Ben Simmons No. 1? What if they get the Lakers' pick, too? And how does the rest of the top 10 shake out? Our Insiders run their latest mock draft, with Philly on the clock.