Boyanov also hauled in 10 rebounds to get his third double-double of the season. Dionte Ferguson contributed 14 points to go with seven rebounds for South Alabama (8-17, 6-8 Sun Belt), which shot 49.1 percent on 55 attempts from the field to snap a three-game skid.
Trailing by three midway through the second half, the Jaguars took the lead for good during a 10-1 burst capped by back-to-back 3-pointers from Johnson and Ken Williams that made it 56-50 with 8:01 left.
Troy (9-14, 4-10) twice cut the gap to four in the final 1:17 but South Alabama protected its advantage down the stretch.
Kelton Ford led the five Trojans in double figures with 17 points.