The Villanova Wildcats hold up the trophy after defeating the...

The Villanova Wildcats hold up the trophy after defeating the Providence Friars in the Big East Tournament championship at Madison Square Garden on Saturday, March 10, 2018. Credit: Steven Ryan

Of course they had to go to overtime. Villanova and Providence had to play some more. Who wanted this to end?

Not just this game and not just this tournament. This entire two-week span in which New York was the capital of college basketball just did not want to say a quick goodbye.

It was appropriate that the two teams playing in the Big East Tournament final should give it their all, should play their hearts out through regulation and into a five-minute extra period that ended with Villanova awash in confetti after a 76-66 win.

“It’s great. We’re at Madison Square Garden: so much history, so much tradition here, it’s amazing,” said Jalen Brunson, who scored 31 points, including two free throws that tied it with 30.1 seconds left in regulation.

That is to say, he had the composure and emotional wherewithal to twice take a deep breath and softly put up a shot that kept the game going.

“Man, I wasn’t even thinking about it,” Brunson said. “I was just thinking, ‘Knock these in, let’s get a stop.’ ”

Which is exactly what happened. Villanova forced Providence star Kyron Cartwright into a miss and then took over in the extra period — at the end of an extra-special fortnight.

In a rare alignment of college hoop planets, the Big Ten, Atlantic Coast Conference and Big East all had their championship tournaments in the same year in the same city. Every bit of it was extraordinary, and it involved the biggest brands in the sport.

Right here, in Manhattan and Brooklyn, we saw Notre Dame come back to win after trailing by 18, Providence come back to win after having trailed by 17. We saw signs of the revival of Boston College. The Battle of Michigan got transplanted here without missing a step: Michigan over Michigan State. Same for the intense Tobacco Road rivalry: North Carolina over Duke at Barclays Center on Friday night.

You didn’t have to be an alumnus (although, trust me, it didn’t hurt) to appreciate the sight of Rutgers lighting the Garden with two surprising wins and a good effort in a loss to Purdue.

In the span of two weeks, we had the four top-ranked teams in the country — highlighted by No. 1 Virginia — all playing breathless single-elimination games in the same town. Quite cool.

That was literally the case for Providence coach Ed Cooley, who felt a cold breeze in the second half. In the excitement, he had split his pants and coached with a towel around his backside. Not a problem.

“Man, this is something you dream about when you’re a kid,” he said. “If you can’t enjoy this moment, on that stage, on this day, Saturday night, you’ve got a problem. We all should be smiling because we’re all very, very fortunate.”

Maybe not all of us. These weeks have been bittersweet for New Yorkers. Sure, it has been a blast to be witnesses and to be such good hosts. But now that March Madness gets going in full stride, New York is a distant observer at best. Unless you count Seton Hall as a New York team and expect it to make a lot of noise, there is not going to be a lot of local flavor in The Big Dance (other than the nice stories of LIU Brooklyn and Iona getting a chance to do a little dancing and dreaming).

St. John’s is a long way from being in the same class as the likes of Villanova, which has a program and a system and a reason to shoot for the national title just about every year.

“I knew, coming here, I would have to sacrifice. I’m playing with all great players,” said center Eric Paschall of Dobbs Ferry, who made big plays on both ends Saturday for Villanova. “I would just say I’m blessed.”

We all could say that, based on seeing what we’ve just seen.