The Braves were behind 47-36 at the half, but were able to rally with the help of Jackson and James Kendrick, who chipped in 17 points.
Sollie Norwood led Texas Southern (7-23, 6-11) with 22 points, David Burrell scored 18 and Matthew Miller added 11.
Alcorn hit 42 percent from the floor and Texas Southern shot 46 percent.
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