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.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.