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.
Alcorn State ended the run when John Gibbs hooked up with Tavoris Doss from 33 yards out, cutting the deficit to 30-11 with 3:52 left to play, but it was far too late to rally.
Ark.-Pine Bluff 42, Prairie View 41
PINE BLUFF, Ark. (AP) -- With Prairie View A&M driving for what appeared would be the go-ahead touchdown, Jarvis Webb forced a fumble and his Arkansas-Pine Bluff teammates recovered deep in their own territory with 1:52 left in the game to sew up a 42-41 victory on Saturday.
Ben Anderson threw three touchdown passes and his 1-yard TD run with 6:41 left in the third quarter gave Arkansas-Pine Bluff (9-2, Southwestern Athletic) a 42-34 lead.
Anderson's scoring passes were to Dezmond Beverly (24 and 10 yards) and Alton Taylor (5 yards).
Prairie View (3-8, 3-6) pulled to within 42-41 with 14:53 left in the game on a 17-yard pass from Jerry Lovelocke to Jacoby Anderson and Chris Barrick's PAT.
Auburn 51, Alabama A&M 7
AUBURN, Ala. (AP) -- Tre Mason rushed for two touchdowns and Onterio McCalebb added two rushing scores to lead Auburn to a 51-7 win over Alabama A&M on Saturday.
Mason rushed for 181 yards and McCalebb ran for 104 yards for the Tigers (3-8).
Auburn ran for a combined 341 rushing yards and finished with 512 total yards, as the Tigers picked up their third win of the season and posted their highest scoring total of the season. McCalebb finished with 142 all-purpose yards.
Mason's two first-quarter touchdown runs, including an 86-yard score, helped give Auburn a 21-0 lead at the end of the quarter, and a 35-0 lead by halftime.
Freshman quarterback Jonathan Wallace finished 10-of-18 for 171 yards passing and on touchdown for the Tigers.
Deaunte Mason went 17-of-28 passing for 186 yards and threw an interception for Alabama A&M (7-4) in the losing effort.
The Auburn defense held Alabama A&M to just 22 net rushing yards on the day, with senior Kaderius Lacey leading the way with 41 yards on 12 carries. Wide receiver Demario Ross led the Bulldogs in receiving with 57 yards on four catches.
Tre Mason's 86-yard touchdown run was the longest by an Auburn running back since Brent Fullwood scored from 88 yards out against Mississippi State in 1986. Auburn's first four touchdowns Saturday came on the ground, capped by a 3-yard touchdown run by fullback Jay Prosch in the second quarter.
Wallace connected with wide receiver Sammie Coates for a 9-yard touchdown pass with 0:23 remaining in the quarter to give to Tigers their 35-0 lead going into the halftime break.
Alabama A&M got on the board with a score on the opening drive of the second half, when Deaunte Mason punched in a 1-yard touchdown.
After another McCalebb score, the Bulldogs gave up a team safety when an errant snap went over punter Chance Wilson's head, and was batted through the end zone.
Auburn sophomore Trent Fisher returned an Alabama A&M interception 60 yards for a touchdown with just under three minutes to play to give the game its 51-7 final score.
The Tigers' 512 total yards were the most by an Auburn team since the Tigers' national championship team totaled 519 yards against Oregon in 2010.
MVSU 34, Texas Southern 3
HOUSTON -- Julian Stafford had an 89-yard touchdown reception and a 95-yard kickoff return for a score as Mississippi Valley State beat Texas Southern 34-3 to finish the season on a three-game winning streak.
The Delta Devils (5-6, 5-4 Southwestern Athletic) also got two defensive touchdowns from Kevin Eugene as they finished with their first winning conference record since 2006. Eugene returned an interception 31 yards for a touchdown and also had a 100-yard fumble recovery.
Stafford had five catches for 160 yards. Brandon Stansell added 102 yards rushing and quarterback Greg Jones ran for 89 yards and a TD for Mississippi Valley.
Texas Southern (2-9, 2-7) had just 241 yards of offense -- compared to 469 by the Devils -- and turned the ball over five times in its final game of the season.