The Tigers (2-3) led by 16 points in the second half before the Braves (1-4) rallied to cut the lead to 53-51 on Donte Thomas' foul shots. But John Davis hit a jumper and Hawkins scored the final seven points as Towson avoided going 0-3 at Charleston this weekend.
Thomas hit a 3-pointer as time expired for the final margin. He led Bradley with 14 points, 10 coming in the second half.
Davis had 14 points for Towson.
Hawkins closed the tournament with another strong performance. The sophomore had a career-high 28 points in Friday's 76-60 loss to Mississippi.
Bradley had its chances against Towson, but the Braves missed five of their next six shots after cutting the lead to two.