Nelson, who went 18-for-31 for 242 yards, threw touchdown passes of 35 and 41 yards to Hannah. Nelson also threw two interceptions.
Hannah caught nine passes for 135 yards and Robert Hersh kicked field goals of 37 and 41 yards for Texas Southern (2-4, 2-1 Southwestern Athletic Conference).
For Jackson State (1-5, 1-2), Trae Rutland threw an 8-yard touchdown pass to Zarian Herring in the second quarter, then scored on a 12-yard run in the fourth quarter to pull Jackson State to within 19-17.
Texas Southern came into the game allowing offenses 380 yards per game, but held Jackson State to 216 total yards.