It was the 15th career interception for Banks -- which ranks second among active players in the FBS -- and third this season.
The Bulldogs led 20-0 at halftime, giving up just 104 yards at that point.
"We're pleased with the win," Mississippi State linebacker Cameron Lawrence said. "But we definitely haven't played our best game."
South Alabama (1-3) lost its first game against a Southeastern Conference opponent. C.J. Bennett completed 14-of-26 passes for 154 yards, one touchdown and one interception. Demetre Baker added 49 yards rushing.
The Jaguars are a transitional BCS team that is in just their fourth season as a program. But they managed to hang close for the majority of the first half before the Bulldogs slowly pulled away.
"I am really proud of this football team," South Alabama coach Joey Jones said. "There are a lot of things we can work on for sure. I saw a lot of heart on that football field tonight. I told the team in the locker room that I can handle (the final score)."
Russell tied a Mississippi State record for consecutive pass attempts without an interception (137) during the second quarter, but then threw an interception on his next throw. It wasn't a great game for the 6-foot-4, 220-pound junior, who looked tentative in the pocket.
"Tyler was making bad reads, offensive line ... it was just sloppy," Mullen said.
While Mississippi State's offense didn't look sharp, the defense did, holding South Alabama without a touchdown until late in the fourth quarter.
It was a reassuring sign for the Bulldogs, whose veteran defense allowed 572 yards in last week's 30-24 victory over Troy.
"Last week was pitiful," Banks said. "We definitely played with a chip on our shoulder tonight."
The game started with an ugly first quarter that ended scoreless. The Bulldogs dropped a few passes, were called for a few penalties and generally looked uninterested against an opponent that was a heavy underdog.
"Every game won't be perfect," Mississippi State receiver Chris Smith said. "It's a learning process."
South Alabama couldn't take advantage. The Jaguars had a chance to take the lead early in the second quarter, but Michel Chapuseaux missed a 47-yard field goal and Mississippi State suddenly shook out of its extended malaise.
"We fought well," South Alabama receiver Jereme Jones said. "It's disappointing that we didn't come out with the W, but we are still learning and we should have things straight by next week."
The Bulldogs needed just three plays to move 70 yards -- capped by Perkins' 44-yard touchdown run -- to take a 7-0 lead with 12:18 left in the second quarter.
Dak Prescott added a 2-yard touchdown run and Devon Bell made two field goals, both from 42 yards, as the Bulldogs built their 20-0 halftime lead.
Top 25 Overview
It was over when... Mississippi State scored 20 in the second quarter to end any suspense.
Gameball goes to... QB Tyler Russell, who only completed 13-of-27 passes for 171 yards and ran in a score.
Stat of the game... 356-347. The Bulldogs coasted and only outgained South Alabama 356-347.