Burwell finished with 12 points for Towson (4-4). His two free throws with 11 seconds showing gave the Tigers a 67-64 lead.
Benimon, Towson's leading scorer on the year, was 11 of 15 from the field and hit 7 of 10 free-throw attempts.
Towson opened an 11-2 lead but watched Vermont cut the deficit to 38-33 at the break and tie it at 40 just 3 minutes into the second half.
Damas scored six of Towson's final nine points.
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point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.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.