Trailing by three, Towson (15-7, 6-3 Colonial Athletic Association) got a pair of free throws from Mike Morsell, followed by Hawkins' go-ahead 3 during a 13-2 run that made it 72-66 with 1:53 left. The Tigers protected the advantage from the foul line, while holding Drexel to 1 of 5 from the field down the stretch to cement the win.
Morsell and William Adala Moto added 16 points apiece for Towson, which shot 50 percent from the field and was 9 of 16 from long range.
Drexel (3-17, 1-8) opened the second half with a 6-0 burst to retake the lead, fending off two Towson drives that tied the game at 54 and 56 before being overtaken.
Sammy Mojica's 17 points led four Dragons in double figures.