Moore ran for 101 yards and completed 18 of 36 passes for 363 yards. Moore connected with Rico Richardson on a 44-yard pass for a touchdown. Richardson caught two other passes for touchdowns.
Texas Southern (1-2, 1-1 SWAC) led 21-14 at halftime, but Jackson State scored 17 points in the third quarter.
Rudolph Johnson ran for a touchdown and completed 11 of 21 passes for 184 yards and three touchdowns. The Jackson State defense sacked him six times. Edward Perkins-Loving ran for a touchdown and Fred Plummer, Tory Allen-Ford and Harry Brown caught passes from Johnson for touchdowns.
The game was the SWAC opener for JSU (1-2). The game was played in Texas Southern's new home, the BBVA Compass Stadium in downtown Houston.