The Tigers (6-4, 6-2 Southwestern Athletic Conference) moved ahead of the Bulldogs (7-3, 6-3) in the Eastern Division race and hold a tiebreaker advantage over Alabama State if they can beat Alcorn State next week.
Moore also ran for a 7-yard touchdown to open the scoring in the second quarter, and Sims's 7-yard scoring run made it 14-0 at halftime.
Alabama A&M halved its deficit in the third quarter, but Jackson State regained control with two big plays.
Bulldogs quarterback Deaunte Mason threw for three touchdowns, but the Tigers limited him to 17 completions in 40 attempts for 193 yards.
The Florida Gators will start Treon Harris at quarterback in Saturday's opener vs. New Mexico State over redshirt freshman Will Grier, coach Jim McElwain said Tuesday.
Oregon State and former coach Mike Riley face a federal Title IX lawsuit filed by a woman who said she was raped as a result of the coach's failure to correct a sexually violent culture.
Los Angeles prosecutors have charged a man in connection with the theft of the University of Southern California's copy of O.J. Simpson's Heisman Trophy more than 20 years ago.
A months-old Facebook post has cost the Nebraska football stadium announcer his job one day after his hiring was announced.
Former running back Lawrence Phillips has been charged with first-degree murder in the April death of his cellmate at Kern Valley State Prison.
Autopsy shows Christian Taylor, a black college football player killed by a cop, had used a synthetic psychedelic drug and marijuana prior to the deadly confrontation.