Tyler Russell completed 13 of 27 passes for 171 yards for the Bulldogs (4-0) while LaDarius Perkins rushed for a team-high 69 yards — including a 44-yard touchdown run.
Nickoe Whitley and Johnthan Banks both had long interception returns that stopped South Alabama drives.
It was the 15th career interception for Banks — which ranks second among active players in the Football Bowl Subdivision — and third this season.
The Bulldogs led 20-0 at halftime, giving up just 104 yards at that point.
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 Bulldogs have a week off before facing Kentucky on Oct. 5.
South Alabama is a transitional BCS team that is in just its fourth season as a program. But the Jaguars managed to hang close for the majority of the first half before the Bulldogs slowly pulled away.
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.
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.
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.
But 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.
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.
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Read more about the game in Sunday's NEMS Daily Journal newspaper.