Even to John Mara’s 14-year-old ears, this sounded a little crazy.

This was late in the morning of Aug. 17, 1969, and the New York Giants’ team bus was negotiating the 18-mile path along I-95 from the team’s training headquarters at Fairfield University to New Haven, where that afternoon they would play the Jets in an exhibition game at 70,000-seat Yale Bowl.

Mara, the eldest of Giants owner Wellington Mara’s 11 children, listened as the players bided their time speaking of the 2 o’clock kickoff in primal terms, odd since this was an exhibition game and wasn’t supposed to count for anything other than local bragging rights between teams that didn’t even play in the same league yet.

“Players were talking about this being the biggest game they had ever played in,” Mara recalled this week. “The tension was unreal. The build-up to that game was unlike anything I had ever experienced, almost like a modern playoff game.”

The Giants had long been the undisputed kings of football New York, beginning with the $500 gamble Mara’s grandfather, Tim, had placed in buying the franchise in 1925. They won four NFL championships and chased all comers — the Brooklyn Lions/Dodgers/Tigers, three different iterations of the New York Yankees/Yanks — out of town.

But the Jets wouldn’t be chased. The AFL had a TV contract, and starting in 1965 the AFL had Joe Willie Namath playing for the Jets. On Nov. 28, 1964, the Giants had the No. 1 pick in the NFL draft and Well Mara fixated on Auburn running back Tucker Frederickson; coach Allie Sherman begged for months for Well to pick Namath instead, and on draft day he finally thought he’d carried the day.

“But then Well called the NFL offices and he told [commissioner] Pete Rozelle that he’d changed his mind and wanted Namath,” Sherman said in a 2003 interview. “Pete said they’d already prepared the press release and Well said, ‘Keep it as is. My word is my word.’ ”

Namath, of course, led the Jets to prominence and then to victory in Super Bowl III while the Giants were stuck in neutral. For years, the Giants dealt with this in a simple fashion: They never spoke of the Jets. They never even pondered the Jets. Mara never once said the name “Joe Namath” in public. And the Giants lorded over their upstart neighbors at every turn.

“We were staying in the same hotel once, and we wanted to get a card game going, and the Giants wouldn’t sit at the same card table with us,” recalled Don Maynard, the Jets’ Hall of Fame receiver who’d started his career as a little-used Giant.

“Giants fans still don’t feel we’re on a parity with their team and we feel we’ve got to prove it,” Jets linebacker Larry Grantham said early in training camp in 1969. “A lot of people, NFL fans, still regard the Super Bowl as a fluke.”

So it wasn’t just the Giants who arrived at Yale Bowl expecting Armageddon. Against a modern backdrop, of course, this is all so laughable: Last week, the Jets and Giants played their annual Snoopy Bowl at MetLife Stadium and every notable player played a series or two at most. The score vaporized from memory as soon as the final gun sounded.

Nothing about this was funny 50 years ago. The local newspapers had been calling for a Jets-Giants exhibition for years, and because the merger between NFL and AFL was already in place, there was no longer a good reason to avoid it. Four charities would split the gate proceeds, but that was the only charitable thing in the Connecticut air that muggy August day.

Jets running back Bill Mathis, an original Titan who’d endured second-class citizenry for a decade, summed it up best: “I want to win even more than the Super Bowl,” he said. Jets coach Weeb Ewank — himself an NFL exile — understood. He appointed Mathis, Maynard and Grantham, the three Jets who’d been there from Day 1, tri-captains for the day.

The Jets went off as four-point favorites. For many, that was not the smart money.

At straight-up 2 p.m., at exactly the moment Jim Turner fixed the ball on a tee for the opening kickoff and booted it to the Giants, 131 miles to the west, Joe Cocker was greeting a sleepy mass of 400,000 in a meadow on Max Yasgur’s farm in Bethel, N.Y., with the first tune of an 11-song, 80-minute set, “Dear Landlord.”

It was Day 3 of the Woodstock Music & Arts Festival, and Day 2 hadn’t ended until around 9:30 Sunday morning when Jefferson Airplane had finished off “White Rabbit.” By the time Cocker completed his performance with his epic cover version of the Beatles’ “With a Little Help from My Friends,” a massive thunderstorm started to move in, shaking the light towers and reducing Yasgur’s field to mud.

Back in Connecticut, another kind of flash storm had already arrived.

And the Giants barely knew what hit them.

There were 70,874 people jammed into Yale Bowl, and at kickoff it was 86 degrees, and if the traffic getting there wasn’t quite the historic mess the long-hairs had crafted over on 17-B and the New York Thruway, it was still a torturous crawl along the Connecticut Turnpike and the Merritt Parkway. The crowd was equally divided. And intense.

“There were multiple fights in the stands,” John Mara said, and it didn’t take long to realize which side would be given more ammunition for the fight. Namath played even better than he had in the Super Bowl, completing 16-of-18 passes for 188 yards and three touchdowns — one of them to a grateful Mathis, who also scored a rushing touchdown.

The Giants, meanwhile, never could get untracked even though they had a golden opportunity on the game’s first drive when, on third-and-5 from their own 33 Fran Tarkenton (9-for-21, 138 yards) spotted Homer Jones streaking all alone down the sidelines for what would have been an easy TD. Tarkenton overthrew Jones.

Next thing you knew, it was 17-0, Jets. And that’s when it got really ugly.

“The Jets,” John Mara said, still unhappy half a century later, “absolutely kicked our butts.”

The signature moment came just before halftime. The Giants’ Dave Lewis punted a ball and … well, let poor 14-year-old John Mara sum it up for you: “The one play I remember was Mike Battle returning a punt for a touchdown and leaping over our punter. The rest I have managed to successfully block out.”

It was 24-0. It ended 37-14. It wasn’t that close. Most Jets, reveling in the day, refused to come out even as the game dragged into garbage time. Namath finally relented with seven minutes left in the fourth quarter. By then, Yale Bowl was filled with a chorus that had been a regular part of the Yankee Stadium set list for years:

GOOD-BYE ALLLIE! GOOD-BYE ALLIE!

GOOD-BYE ALLIE, WE HATE TO SEE YOU GO …

On the sideline, Maynard giddily joined in the sing-along. And this time, the masses got their wish. Well Mara waited until a few weeks later, following a lifeless exhibition loss to the Steelers in Montreal, before finally firing Sherman. But everyone knew what the impetus had been.

“I got fired for losing to the quarterback I coveted all those years,” Sherman said in ’03, able to smile about it by then. “Ain’t that a kick in the pants?”

For the Jets, who’d earned $15,000 a man for winning Super Bowl III, the $250 each they received for playing the Giants was a happy bonus. They’d come to Connecticut to make a statement. And they made it.

“Today we proved we have the best team in New York, a team that can compete on any field with any team at any time,” Grantham said.

Said Namath: “We played as hard as we did in the Super Bowl.

“There’s no doubt who’s No. 1 in New York now. The score proves who’s No. 1.”

Said Jets running back Matt Snell: “Give us money or give us prestige to play for and we’ll go. I mean you saw what we did out there today. You know it wasn’t the $250 we earned that made us do it, so it had to be the glory. And, man, was it glorious today.”

All these decades later, even as the Giants have added four Lombardi Trophies to their collection while the Jets’ total remains frozen at one, there is one former 14-year-old kid who still chafes at what happened in the Yale Bowl 50 years ago Saturday.

“It’s not one of my happier memories,” John Mara said. “Thanks so much for bringing it up.”