The Tigers (16-13, 11-5 Colonial Athletic Association), who were 1-31 last season, won for the sixth time in seven games.
A three-point play with 1:20 remaining by Benimon, who recorded his 19th double-double this season, gave Towson a 71-68 lead. Derrick Thomas' layup for the Dragons (11-17, 7-9) with 1:01 left cut it to 71-70.
Hairston stole the ball from Damion Lee with 11 seconds left and was fouled but made just 1 of 2. Kazembe Abif was fouled after getting an offensive rebound on Drexel's next possession and could have tied the game but was also able to make only 1 of 2.
Frantz Massenat scored 24 points to pace the Dragons. Thomas added 13 and Lee 12.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
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