Devin Carter added 20 points on 5-for-9 shooting from 3-point range.
Arkansas State (6-7, 2-0 Sun Belt) led 35-33 at the half. But the Red Wolves used a 12-3 run in the first four minutes after the break to make it 47-36.
South Alabama (5-8, 0-2) responded with Georgi Boyanov's layup and back-to-back 3s by Ken Williams to cut its deficit to 49-44. The Red Wolves countered with Livingston's jumper and Carter's three consecutive 3-pointers in a two-minute stretch to extend their lead to 60-46, which was never challenged.
Williams finished with 23 points for South Alabama.
Arkansas State raced to a 12-2 lead, which grew to 24-9 on a Carter 3 with 11:40 left, but the Jaguars outscored Arkansas State 24-11 to close the gap.