Brandon LaFell had 101 yards and two touchdown catches and Chad Jones scored on a 93-yard punt return for the Tigers (4-0, 2-0 SEC).
Anthony Dixon couldn't score on two attempts from inside the 3 with a minute to go. LSU then stuffed quarterback Tyson Lee on fourth and inches.
It was the Tigers' 10th straight win over the Bulldogs (2-2, 1-2), who gave up four big plays that proved costly.
Patrick Peterson returned one of Lee's three interceptions for a 37-yard touchdown on Mississippi State's first offensive play. LaFell caught a 58-yard score on LSU's first play of the second half, and Jones went from sideline to sideline on his return.
Dixon scored twice to become the Bulldogs' career leading scorer and moved into second on the school's career rushing yards list. But he couldn't add one more touchdown that would have put Mississippi State ahead late.
It's been a lopsided series for the last two decades, with the Tigers winning 17 of 18. LSU outscored Mississippi State 374-105 in the previous nine games and held the Bulldogs to 13 points, with two shutouts in its last four visits to Starkville.
But the Bulldogs showed they may be closing the gap.
LSU, which sat on the tarmac in Baton Rouge, La., on Friday for more than four hours and missed its walkthrough, opened the game listlessly on offense and had nearly as many penalties in the first half (6) as rushing yards (7).
Mississippi State helped keep LSU in the game, though, with four turnovers in the first two quarters that led to 10 points.
The Bulldogs responded quickly after Peterson's touchdown return and a missed extra point with a long drive and Dixon's first score, a 2-yard run out of the wishbone.
LaFell shook his defender for a 5-yard touchdown catch on the next series before Dixon's second short scoring run put the Bulldogs ahead again. Josh Jasper's 22-yard field goal gave the Tigers a 16-14 halftime lead, and LaFell and Jefferson wasted no time adding to it.
After LSU forced Mississippi State to a three and out on its first series, LaFell shook his defender deep and Jefferson hit him in stride for an easy score.
Lee answered with a 50-yard scoring pass to cut it to 23-21 midway through the third quarter.
After the Bulldogs' next drive stalled shy of midfield, coach Dan Mullen called a timeout to discuss punt coverage. It appeared Heath Hutchens tried to kick away from Jones, but he ran to his left to field the ball and Mississippi State's coverage unit overcompensated.
Jones broke two tackles around his own 10, cut across midfield, tripped on his own blocker around the 50, but managed to slip past Hutchens and stay upright the rest of the way.
The Bulldogs got the ball back at midfield with 3:53 left. Dixon's 18-yard run put them at the 2 with more than a minute to go.
LSU's front seven stuffed Dixon twice out of the wishbone, then forced an incomplete pass on third down. Lee took the snap on fourth down from less than a yard out. He took a drop step to fake a handoff, then turned back to the line of scrimmage, where he was met by the Tigers for no gain.
Read more about this game in Sunday's NEMS Daily Journal.