South Alabama (7-14, 5-5 Sun Belt) trailed by 10 points at the half, 43-33, but eventually pulled ahead on a pair of free throws by Johnson, followed by Barrington Stevens' jumper that made it 64-60 with 7:31 left.
Shawn Long made a pair of 3-pointers, the second with 32 seconds left, to pull the Ragin' Cajuns within two. But the Jaguars made 6 of 8 free throws inside of 31 seconds to seal the victory.
Johnson was 6 of 10 from the floor and 9 of 10 from the line. Ken Williams had 19 points while Stevens finished with 17 points, seven boards and six assists. Dionte Ferguson chipped in 16 points with four blocked shots.
Long paced Louisiana-Lafayette (11-10, 5-5) with 26 points and 12 rebounds. Kasey Shepherd added 20 points with five 3-pointers.