TUSCALOOSA, Ala. — Here it was, with Bryant-Denny Stadium in full-throated roar and Alabama charging hard — just as the Crimson Tide always do, having risen once again from the coroner’s slab — so Louisiana State did what it has done in every moment that has mattered this season.

It put the ball into the hands of Joe Burrow, a senior quarterback with spindly legs, a baby face and a cold, cold heart.

Burrow delivered time and again in the fourth quarter, with his arm, his legs and, more than anything, his poise, helping lead L.S.U. to a 46-41 victory that more than lived up to its considerable hype before a capacity crowd of 101,821 that included President Trump.

Trump, in fact, may have been the only person in the stadium who did not stay until the end to witness Burrow and the determined running of halfback Clyde Edwards-Helaire, who busted through Alabama tackles on both of his fourth-quarter touchdown runs that held the Crimson Tide at bay.

The win, which snapped Alabama’s 31-game winning streak at home, will surely push the unbeaten Tigers to the top of the College Football Playoff rankings, ahead of No. 1 Ohio State and Clemson and who knows who else after previously unbeaten Penn State was upset at No. 17 Minnesota on Saturday.

As the Tigers sauntered over to their band afterward, dancing along to “Hey, Baby” with the sliver of the crowd that was purple and gold, they did so having extinguished a boogeyman — and with extraordinary offensive panache.

L.S.U. had lost to Alabama eight consecutive times, dating back to the 2011 national championship game. And after the Tigers had watched their offense so often be ground down by the Alabama defense, they eviscerated the Tide this time, rolling up 559 yards and scoring more points than they had in their last five losses to Alabama.

L.S.U. Coach Ed Orgeron, who calls his team’s film sessions at the start of each week Tell The Truth Mondays, told the news media after last year’s 29-0 loss to Alabama that his team had been manhandled. Going into this matchup, he told his players that the Tigers were the better team.

“It was like, ‘Hey, you know what? It’s not overwhelming,’” Orgeron said. “This is something we can do, even though we’re on the road. We’re well equipped. I felt good getting on the plane.

“I said, ‘You know what? Our guns are loaded. We comin’. ’”

The Tigers needed every bit of that brilliance from their transformed offense to stave off Alabama, which charged back from a 20-point halftime deficit.

If the game had continued like that, the beloved Tide might have been treated more rudely than Trump.

After being booed heartily at a World Series game in Washington and then again at a mixed martial arts event in Manhattan in the last two weeks, Trump found a more hospitable crowd on Saturday. He was greeted with an enthusiastic ovation when he was shown with his wife on a video board during a timeout in the first quarter. He smiled and waved to the crowd.

Alabama has exerted a magnetic pull on Trump.

It was here two years ago that he blasted N.F.L. players who knelt during the national anthem. And in September, when his weather forecasting skills were widely ridiculed for indicating that Hurricane Dorian could hit Alabama, Trump displayed a forecasting map that drew more ridicule because it was altered with a marking pen.

His presence on Saturday meant handling a massive crowd — an estimated 50,000 turned up to watch outside the stadium — with security befitting a Super Bowl. Fans traveling from Birmingham and elsewhere were advised to arrive early, and the gates were opened more than three hours before kickoff to ensure fans had enough time to get into the stadium.

The disruptive behavior that Alabama students were warned against earlier in the week at the risk of losing their football seats — a threat that was later walked back — never materialized. The stakes of the game — and the tension that it carried down the stretch — largely relegated Trump’s presence to a footnote.

Instead, it was Burrow, the senior transfer from Ohio State, who carried the day.

Burrow has been dynamic in the Tigers’ biggest games this season — wins at Texas and home against Florida and Auburn — and was even better against Alabama. He was elusive and decisive, and when he wasn’t delivering darts to his receivers, he was torturing the Tide with soul-crushing runs.

At the end, he was carried off the field by his teammates.

“This is why I decided to transfer,” said Burrow, who was stuck behind Dwayne Haskins at Ohio State. “I wanted to play, and I knew I could play on this stage and, you know, I got great people around me, great coaching staff, great program all around.”

Burrow was also at his best when he needed to be, after Alabama charged back to within six points early in the fourth quarter. But Burrow calmly converted three third downs. The first came when he hit Justin Jefferson on a slant on third-and-3 and the last when he raced for 15 yards on a draw.

But the most impressive came when, with a blitzer in his face, Burrow dumped the ball to Edwards-Helaire, who bulled his way through the safety Xavier McKinney for 11 yards on third-and-10. Edwards-Helaire finished the drive by tormenting McKinney again, dancing out of his grasp in the backfield and coasting into the end zone for a 5-yard touchdown run with 10:07 left for a 39-27 lead.

After Alabama closed within 39-34 on a 5-yard touchdown pass from Tua Tagovailoa and an extra point with 5:32 to play, Burrow went to work again. He quickly hit Ja’Marr Chase for 29 yards over the middle; with the defense keying on Edwards-Helaire, Burrow kept the ball on a third-and-2 keeper for 18 yards.

Edwards-Helaire, listed at 5-foot-8, 208 pounds, then broke two tackles on the next play for his third rushing touchdown. He rushed 20 times for 103 yards.

“He plays like he’s 6-4, 270,” Orgeron said. “He walks in the room like he’s 6-4, 270.”

Burrow, though, was scintillating. He completed 31 of 39 passes for 393 yards and three touchdowns, along with 64 yards rushing on 14 carries. He further solidified his standing as the Heisman Trophy front-runner, distancing himself from a field that includes Tagovailoa, who returned three weeks after an innovative surgery for a sprained ankle — the same procedure he had on his left ankle last December after the Southeastern Conference championship game. Tagovailoa returned from that game and played superbly in a 45-34 win over Oklahoma in a playoff semifinal.

He was not the same player on Saturday.

“He was a warrior, in terms of what he did,” Alabama Coach Nick Saban said. “I think probably missing the practice that he missed over the last couple weeks, he may not have been quite as sharp as normal.”

Tagovailoa wore a sleeve on his lower right leg, but his oft-impeccable accuracy turned spotty, and he was cautious running with the ball. The magic he conjured in the national championship game two years ago — coming off the bench as a freshman to lead Alabama to a comeback win over Georgia — was largely absent.

On Saturday when he moved Alabama crisply down the field to open the game, he dropped the ball as he tried to juke his way near the end zone. Ray Thornton pounced on it for L.S.U. at the 8-yard line.

It was the first of several self-inflicted wounds for Alabama, which has built a reputation —‚ and a dynasty — under Saban by not beating itself.

But the freshman punter Ty Perine had a snap go through his hands and when Burrow threw an interception shortly after, it was negated because Alabama had 12 men on the field. In the waning seconds of the first half, Tagovailoa threw an interception deep in his own territory and guard Landon Dickerson compounded the mistake with a personal foul penalty.

Burrow hit Edwards-Helaire for a 12-yard scoring pass on the next play that carried the weight of a haymaker. Stunningly, L.S.U. led 33-13.

It wasn’t over, of course, but eventually Burrow saw to it that it was.

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