Sims led Jackson State's rushing attack with 152 yards on 26 carries. His 46-yarder in the fourth quarter created the final margin.
Gooden added 64 yards on eight carries and scored touchdowns of 11 and 28 yards on back-to-back third-quarter possessions for the Tigers (7-4, 7-2 Southwestern Athletic Conference).
Alcorn State (4-7, 4-5) got on the board first after Ernesto Santillan converted a 37-yard field goal. But Clayton Moore connected with Rico Richardson for a 37-yard touchdown, sparking a 30-point spurt for the Jaguars.