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.
Charles Matthews, who spent his freshman season at Kentucky, has picked Michigan as his transfer school, according to a source.
Chad Ford and Jeff Goodman offer their opinions on the surprises they're expecting at the NBA draft, with Ford believing there will be a lot of trade activity while Goodman thinks people will be surprised by potential draft spot of Marquese Chriss.
Louisville coach Rick Pitino said he doesn't "have time to figure out what" Kentucky coach John Calipari meant in recent comments that appeared to be a jab at the Cardinals' program.