Tom Cruise sure picked a heck of a night to attend his first college football game.

And he may have drawn some inspiration if he is ever called on to play a quirky football coach whose team has to overcome some big and at times self-inflicted adversity.

The famous actor, in New Orleans to film a “Jack Reacher” sequel, was perched in Joe Alleva’s booth Saturday night, taking in the spectacle that was the huge Southeastern Conference showdown between LSU and Florida.

What he witnessed was a classic game of SEC survival. Two titans going at it blow for hammer blow.

“Days of Thunder,” you might say, with the Tigers surviving the Gators’ last Hail Mary to pull out a flawed but fabulous 35-28 victory.

After 5-0 LSU beat 6-0 Florida and 5-1 Alabama dusted off Texas A&M 41-23 in College Station on Saturday, LSU was the last SEC unbeaten still standing.

LSU steps out of conference to play Western Kentucky next week, a team led by the nation’s leading passer, Brandon Doughty, who will no doubt test an LSU secondary that is either playing smothering coverage or getting busted for big gains.

But that will only be prologue to what everyone knows is coming after that: yet another November showdown with Alabama for SEC domination.

“War of the Worlds,” you might say.

That will be a huge game spiced with College Football Playoff overtones, but it will be hard to top the rags to riches to rags to grand larceny storyline of this night.

“That,” Florida coach Jim McElwain said, “was a great college football game.”

In just the first half, LSU piled up 28 points, more than the Gators’ vaunted defense had given up in any game this season. The Tigers racked up 304 total yards, more than Florida gave up on average in its first six games, all wins.

Of course, there was still drama. This is still LSU. There had to be drama. “A Few Good Men” kind of drama. “Born on the Fourth of July” kind of drama.

A muffed punt by Tre’Davious White set up Florida’s first touchdown, the first time this season LSU had fallen behind by seven points. Then there were blown coverages by the Tigers secondary, a recurring theme this season, which helped the Gators motor quickly to touchdowns just before and after halftime as backup Treon Harris completed passes at a rate that was thought to be far above his scholarship grade.

Still, LSU held what looked like a commanding 28-14 halftime lead thanks to an awakening of the Tigers’ passing game against the highly regarded Florida secondary.

Brandon Harris hit a big flea flicker to Malachi Dupre to set up a Leonard Fournette touchdown, then spun away from pressure to find Dupre on an improbable 50-yard touchdown pass just 15 ticks before the halftime gun.

But LSU couldn’t put Florida away, and the Gators, true to the revivalist theme of their season, came roaring back. Kelvin Taylor scored on a 2-yard run set up by more uncovered LSU pass coverage, then Antonio Callaway ran right up the gut of LSU’s punt coverage team for a 72-yard return that tied the score at 28.

The Gators had all the momentum. A sold-out Tiger Stadium was as silent as the grave. Holding on for LSU seemed to be, dare we say it, “Mission: Impossible?”

Not so fast, Lee Corso style. Out of nowhere, the Mad Hatter showed one of his unpredictable cards.

LSU looked stalled at the Florida 16 with just under 11 minutes left and sure to kick a field goal to try to break the 28-28 deadlock. But Les Miles called for a fake instead as holder Brad Kragthorpe, a walk-on quarterback, tossed a lateral to kicker Trent Domingue, who motored untouched for the touchdown despite admitting he was so nervous that he blacked out — yes, blacked out — on his way to the end zone.

He recovered enough to kick the extra point.

“Risky Business,” indeed.

“It’s kind of a badge of honor. They’ve got to fake one to beat us,” McElwain said defiantly.

Ex-Florida coach Urban Meyer can relate. The call was reminiscent of LSU’s fake field goal at Florida in 2010, when kicker Josh Jasper caught a lateral on a hop and made a first down late in a thriller in Gainesville.

That gutsy call set up the winning touchdown that night. This gutsy call was the winning touchdown as LSU’s defense found just enough gumption to stop the Gators on two drives and preserve the win.

It was such a classic victory for LSU under Miles: hugely flawed, heartpoundingly exciting, completely unforgettable.

What kind of night did LSU Heisman Trophy frontrunner Leonard Fournette have, asked to run and run and run against a top-notch defense primed to stop him? He piled up 180 yards and two touchdowns on a career-high 31 carries.

“Legend.” And his Heisman lead seems secure for another week.

As for our friend Tom Cruise, who was high-fiving Alleva’s wife, Annie, after Brandon Harris’ first touchdown pass to Dupre, he came away from Tiger Stadium impressed.

“Memorable. Exciting,” he told our Ross Dellenger after they shared an, ahem, halftime bathroom break. “Everything else will pale in comparison.”

We assume he means his next college football game, not the rest of his movie career.

Then again, maybe not.