The victory was the seventh in a row for the Catamounts (16-10, 10-2 America East Conference), who remained one game behind first-place Stony Brook.
Brendan Bald scored 11 of his 13 points in the first half to help Vermont lead 37-25 at the break.
The Black Bears (11-11, 5-6) closed to within 45-41 with a 9-0 run, but baskets by Apfeld and Brian Voelkel pushed the Catamounts' lead back to eight points, and they led by at least six the rest of the way.
Voelkel finished with nine points, nine rebounds and seven assists, and Vermont's 16th win gave John Becker a record for first-year coaching wins at the school.
Gerald McLemore scored 20 points and Justin Edwards 15 to lead Maine.
- America East Conference