The No. 3 Tigers held Eli Manning and the high-scoring Rebels in check for three quarters, then withstood a fourth-quarter rally to earn a 17-14 victory Saturday.
Matt Mauck threw two touchdown passes for LSU (10-1, 6-1), which now controls the SEC West race and can clinch its second trip to the conference title game in three years with a victory over Arkansas.
The Tigers were fourth in the latest bowl championship series standings, but with Ohio State's loss they are poised to move up a spot.
"It wasn't pretty, but our character and maturity showed," LSU Coach Nick Saban said. "Their defense really played well too. It's a shame somebody lost, but I was definitely relieved to get the W."
Ole Miss (8-3, 6-1) had its chances to pull off a second consecutive fourth-quarter comeback victory.
Jonathan Nichols, who had missed only one of 24 field-goal attempts coming in, was wide right on a 36-yarder that would have tied the game at 17 with 4 minutes 15 seconds left.
It was Nichols' second miss of the day.
"Everything was perfect," Nichols said. "I thought I hit it real good. When I looked up, it faded right on me. Man, it's not a good feeling."
The Rebels got one last chance with 2:15 left, but Manning was incomplete on three consecutive passes and on fourth down he was tripped pulling away from center.
Manning completed 16 of 36 passes for 200 yards with a touchdown and an interception. He was sacked three times.
"They were bringing pressure, and we were trying to react to it and just didn't make plays," Manning said.
Ole Miss can still win the SEC West if LSU loses its season finale and the Rebels beat Mississippi State.
Mauck completed 16 of 29 passes for 189 yards, but three interceptions helped keep Ole Miss close while it gained only 98 yards through the first three quarters.
Travis Johnson picked off Mauck's pass on LSU's first play and returned it six yards for a touchdown to give Ole Miss a 7-0 lead.
The Rebels, who lead the SEC in scoring at 37 points per game, didn't score again until the fourth quarter.
"Our defense has been doing this all year," LSU defensive tackle Chad Lavalais said. "We were fortunate, like when that last field goal was no good, but you need that. But it's not luck, because we've been doing it all year."