Jacksonville State's Troymaine Pope ran for 234 yards, the second-highest total in school history, and three touchdowns. Jenkins threw for 208 yards, going over 5,000 in his career, and an interception and ran for 195 yards and three scores.
Jacksonville State had a 14-point lead in the third quarter but the Mocs (9-4) rallied to go ahead 35-28, their final score coming with 8:35 left when Huesman passed to Alejandro Bennifield who threw back to the quarterback for a 39-yard score.
The Gamecocks tied it with 4:40 remaining on Pope's 75-yard run.
Huesman passed for two touchdowns and ran for two.
The Gamecocks (11-1) play Charleston Southern in the next round.