Ballard found Ledarion Heath for a 37-yard score finishing a seven-play, 77-yard drive early in the first quarter to give Alabama A&M (3-8, 3-6 Southwestern Athletic Conference) a lead that wouldn't be contested.
Early in the second, Harvey Harris had a 29-yard touchdown run to make it 14-0.
Texas Southern (3-7, 2-7) scored when quarterback Averion Hurts ran 4 yards to cut the lead to 14-7 but the Tigers could get no closer.
Alabama A&M's Brandon Eldemire had 17 carries for 102 yards and a score. Jonathan Dorsey also scored for the Bulldogs.
Hurts threw for 89 yards and an interception while Darrell Robinson had nine carries for 83 yards.