The Crimson Tide only slipped one spot to third.
If the Tigers (9-0) and Cowboys (9-0) remain unbeaten, they should meet in the New Orleans on Jan. 9.
If either slip up, Alabama or fourth-place Stanford are in position to reach the title game as long as they keep winning.
Tigers top AP poll. Louisiana State put a lock on the top spot, Oklahoma State moved up to No. 2 for the best ranking in school history, and Alabama slipped to No. 4 in the Associated Press Top 25 poll on Sunday.
Penn State, idle and mired in an off-field scandal, moved up four spots to No. 12.
LSU received 59 out of 60 first-place votes. Oklahoma State moved up one spot, while Stanford inched up to No. 3.
Alabama slipped two spots. Boise State remained No. 5 with one first-place vote.
LSU, Oklahoma State, Stanford, Boise State, and No. 11 Houston are the remaining unbeaten teams in major college football. The Cougars (9-0) have their best ranking in the AP poll since 1991.
The rest of the top 10 was No. 6 Oregon, followed by Oklahoma, Arkansas, Clemson and Virginia Tech.
Saban rues missed chances. Saturday's "Game of the Century" between LSU and Alabama turned into a game of inches - and of poise under pressure. The top-ranked Tigers made the kind of plays that can sometimes preserve national title hopes. The fourth-ranked Crimson Tide didn't do that in defeat.
Tide coach Nick Saban said missed chances were "the difference in the game."
LSU's secondary came up with game-changing interceptions by Eric Reid and Morris Claiborne.
Alabama not only had four missed field goals but botched a late punt return and had a block in the back on an interception return that would have set the Tide up inside the Tigers 5.
Ratings win. The game drew the second-highest rating of any CBS regular-season college football broadcast since the network began tracking ratings in 1987.
The network said Sunday the No. 1 vs. No. 2 showdown earned an average overnight rating/share of 11.9/21, up 170 percent from last year's game.
The highest-rated CBS regular-season game is Miami's 1989 win over Notre Dame.
Boise State perfect, but . . . A 48-21 win at UNLV Saturday night - with Kellen Moore throwing five touchdowns and passing ex-Texas star Colt McCoy as college football's winningest quarterback - wasn't enough to push No. 5 Boise State any higher in the AP Top 25 despite Alabama's loss.
That's partially because the Broncos (8-0) weren't convincing in their win over the Rebels.
Boise State didn't really get its running game going until the fourth quarter, as D.J. Harper and Drew Wright each scored a touchdown. The backs combined for 21 carries on 156 yards.
Ducks impress. Oregon's defense showed up with one of its more impressive performances of the season in a 34-17 win over Washington on Saturday night.
But the Ducks' effort again featured plenty of offensive highlights. LaMichael James looked fully healed from an elbow injury suffered early last month, running for 156 yards and a touchdown.