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.
Andy Katz breaks down the likelihood of Villanova, Syracuse, North Carolina or Oklahoma making a run to the Final Four next season.
Florida State has announced that Xavier Rathan-Mayes will return to the court for his junior season. The 6-foot-4 guard declared for the NBA draft last month but did not hire an agent.
Virginia coach Tony Bennett takes the ACC Fast Break with Dino Gaudio by answering questions like who the best Tony Bennett is and what other sport he'd like to coach.