Vermont (20-11) trailed 22-14 at halftime after shooting just 6 of 25 from the field in the first half. The Catamounts, however, used a 24-10 run to take a 38-32 lead with 4:44 remaining.
Raheem Singleton's jumper helped Maine cut the deficit to 43-40 with 1:28 left to play, but Glass made a layup and Apfeld and Four McGlynn combined to sink five free throws in the final minute to seal the victory.
Alasdair Fraser led Maine (12-16) with 10 points, but the Black Bears shot just 32 percent (17 of 53) from the field and missed all 17 of their 3-point attempts.
Vermont was 14 of 17 from the free throw line, taking 10 more free throws than Maine.