Augustine Rubit finished with 19 points and nine boards, and Freddie Goldstein scored 11 for South Alabama (4-3, 2-0).
Antoine Allen came off the bench for the Jaguars to connect on all three 3s, finishing with 13 points.
Tied at 16, South Alabama went on a 14-4 run spurred by back-to-back 3s by Ammons.
Ammons finished the first half with 12 points, going 4 for 6 from the 3-point line as South Alabama led at halftime 41-33.
South Alabama shot 57.9 percent (11 for 19) in the second half to pull away from FIU (2-3, 1-1), which shot just 30.8 percent (12 for 39) in the second half.
Tymell Murphy finished with a double-double, 16 points and 10 rebounds to lead FIU.