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.