Troy had a 31-25 halftime lead, but South Alabama used a 28-14 run to start the second half and led 53-45.
Troy's Jeremy Hollimon, who finished with 14 points, nailed a 3-pointer to close to 53-51. Boyanov answered with two free throws and Ken Williams scored six straight points to give South Alabama a 61-56 lead.
Troy's B.J. Miller had a layup to pull to 61-58 with 44 seconds left. Boyanov responded with a trey and followed with a dunk to seal it.
Boyanov was 7 of 15 from the floor and grabbed 10 rebounds for the Jaguars (8-12, 3-6 Sun Belt Conference). Williams finished with 11 points and Shaq Calhoun added 10.
Wesley Person had 15 points for Troy (6-14, 1-8).