LSU staked its claim to being the No.1 team in the nation on Saturday, while Joe Burrow staked his claim to the Heisman Trophy.

Before a crowd of 101,821 at Bryant-Denny Stadium in Tuscaloosa, Ala. -- including the president and first lady -- Burrow completed 31 of 39 passes for 393 yards and three touchdowns as LSU knocked off Alabama 46-41 in the first regular-season matchup between the top two teams in the Associated Press poll since the Tigers and the Tide squared off in 2011.

"He's one of the best we've had here," LSU coach Ed Orgeron said. "But we've still got four games left and we're going down the road, we're going to try to win every game and we're going to bring a championship back to Louisiana."

The Tigers, ranked second in the College Football Playoff rankings, appeared be in full control of the game after a 23-point second quarter in which Burrow threw for two touchdowns and Clyde Edwards-Helaire (180 all-purpose yards, four total TDs) ran for a score and caught one of Burrow's touchdown passes. The duo's 13-yard hookup gave LSU a 33-13 lead at halftime, the largest deficit a Nick Saban-coached Crimson Tide team had faced after 30 minutes.

Clyde Edwards-Helaire scores for LSU in the first half of Saturday's game. (Associated Press)

But Alabama, specifically Najee Harris (190 total yards, 2 TDs), responded like champions. First, Harris caught a 15-yard third-quarter touchdown pass from Tua Tagovailoa, who was 20 days removed from ankle surgery and looked well shy of 100 percent. Then, Harris powered over from one yard out early in the fourth quarter to bring the Tide (ranked No. 3 by the playoff committee) within 33-27.

But then it was Burrow's turn. The Ohio State transfer guided the Tigers 75 yards in 12 plays, scrambling for 15 yards on a crucial third-and-five before Edwards-Helaire turned the corner to score from five yards out.

Ja'Marr Chase catches a touchdown pass from Joe Burrow for the first score of Saturday's game. (Associated Press)

Tagovailoa hit Jerry Jeudy for a five-yard touchdown on fourth-and-two to bring Alabama to within 39-34, but the Tide's defense could not stop Burrow and Edwards-Helaire. The two led LSU on another 75-yard march that was capped by a seven-yard touchdown run for Edwards-Helaire. On the preceding play, Burrow ran around Alabama's right end to pick up 18 yards on a third-and-two.

"We're not done yet," the two-year starting QB said. "It's Game 9. We've got three more regular-season ones and the SEC championship. This was never our goal. We've got bigger goals than this."

With the score 46-34 with 1:37 to play, Tagovailoa (who finished 21-for-40 for 418 yards, four touchdowns, an interception and a fumble) hit DeVonta Smith for an 85-yard touchdown pass that provided the final margin. Justin Jefferson recovered the ensuing onside kick and LSU could start a celebration eight years in the making.

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Coach Nick Saban said Tagovailoa practiced all week without any issues.

"He said he could play in the game, he wanted to play in the game and he thought he could go out and do a good job," Saban said. "I think he was a warrior in terms of what he did."

The win was LSU's first over Alabama since that 2011 showdown, which the Tigers won 9-6 in double overtime. The 46 points are the most LSU has scored against Alabama, and seven more than the Tigers had managed in the last five meetings combined.

The Associated Press contributed to this report.