The Catamounts (6-8) hit 34 of 41 free throws to secure the win. Dartmouth (7-5) was 10 of 12 from the line.
Voelkel made all eight of his free throws, Rugg was 10 of 12 and Sandro Carissimo went 9 of 10 to make up for going 1 of 10 from the field.
Vermont scored 15 points from the foul link in taking a 30-22 lead at halftime. Dartmouth, which was averaging 75 points a game, started 0-11 from 3-point range but, hit 3 of its next 5 to stay in the game after falling behind by 11. They finished 3 of 18 and shot 35 percent for the game.
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point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.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.