But the Gamecocks scored the game's final 14 points to pull away for a 31-16 Ohio Valley Conference victory in front of nearly 17,000 fans at Burgess-Snow field in Jacksonville, Ala.
Southeast fell to 2-3 overall and 1-1 in OVC play. JSU, ranked 24th nationally, improved to 2-2 and 1-1.
The Gamecocks are 9-1 against Southeast since they joined the OVC in 2003 although the previous two meetings between the squads had been decided by a total of three points.
Saturday's matchup looked like it might follow that trend when the Redhawks pulled within 17-16 on senior tailback Renard Celestin's 13-yard touchdown run on the first play of the fourth quarter.
Southeast failed to tie the contest, however, as senior kicker Drew Geldbach's extra-point attempt sailed wide left. It was Geldbach's first missed PAT of the season.
JSU came right back with a 73-yard drive that culminated in a 20-yard touchdown pass from senior quarterback Marques Ivory to senior wide receiver Alan Bonner with 10 minutes, 57 seconds left.
The Gamecocks were flagged for an illegal block on the play, which would have negated the touchdown. But the officials, after conferring, picked up the flag so the TD stood as JSU went ahead 24-16.
Southeast was forced to punt on its next possession and JSU iced the victory with a 61-yard drive that ended on an 8-yard touchdown run by sophomore tailback DaMarcus James with 2:05 left.
"It was one of those games where I felt we could take over at any time and I'm sure they felt the same way," Southeast coach Tony Samuel said. "It was two ground-and-pound style offenses going at it."
Things began well for the Redhawks. After forcing a JSU punt on the game's opening possession, Southeast was pinned at its 1-yard line.
The Redhawks marched 99 yards in 13 plays. Sophomore fullback Brandon Beck, a Jackson High School graduate, scored his first collegiate touchdown on a 5-yard run to put Southeast up 7-0 with 5:30 left in the opening period.
JSU tied things with an 84-yard drive that ended when Ivory hit senior wide receiver Kevyn Cooper on a 14-yard scoring strike with 1:12 remaining in the quarter.
Both squads exchanged punts before the Redhawks grabbed their final lead of the day on Geldbach's 42-yard field goal, making it 10-7 with 6:21 to play before halftime.
Geldbach is 8 of 9 on field goals this season.
The Gamecocks regained the lead by driving 72 yards for a touchdown with just 1:24 remaining before the break.
James did the honors on a 1-yard plunge as JSU carried a 14-10 advantage into the locker room.
JSU, after forcing a Southeast punt on the opening possession of the second half, failed to take advantage of a golden opportunity.
The Gamecocks marched to a first-and-goal at the Southeast 4-yard line but three running plays netted just one yard as the Redhawks' defense stiffened.
JSU settled for a 20-yard field goal to make it 17-10.
Southeast then drove 70 yards for Celestin's touchdown that pulled the Redhawks within 17-16 before the PAT failed and JSU grabbed control.
Southeast senior tailback Levi Terrell had his second straight 100-yard rushing performance and third this season, piling up 146 yards on 26 carries. He has 590 yards this year.
"Levi ran well and you have to give him a lot of credit," Samuel said. "He pushed through a lot."
Redshirt freshman quarterback Scott Lathrop added 54 yards rushing on 17 attempts. He completed 7 of 11 passes for 56 yards.
Sophomore wide receiver Spencer Davis caught four passes for 28 yards.
JSU outgained Southeast in total yardage 429 to 303. Both teams ran the ball well, the Gamecocks posting 268 yards rushing compared to 247 for the Redhawks. JSU averaged 5.5 yards per carry, with Southeast at 4.6.
James rushed for a career-high 149 yards on 21 carries. Ivory completed 14 of 18 passes for 161 yards. Bonner had seven receptions for 92 yards.
Neither squad committed a turnover in the well-played game that also featured only eight combined penalties.
Southeast was penalized just three times for 20 yards. JSU was flagged five times for 44 yards.
An area that Southeast continued to struggle in was stopping opponents on third down.
JSU was 10 of 13 on third downs as the Redhawks are allowing the opposition to convert 57 percent.
"Any time you start seeing that you'll have an issue," said Samuel, whose offense was strong in that area, converting 8 of 14 third downs.
Junior safety Ben Kargbo led Southeast's defense with a career-high 11 tackles. Senior safety Tylor Brock had 10.
Southeast is off next week before hosting Tennessee State on Oct. 13.