NEW YORK — They wanted to move them.

They tried to contract them.

And the baseball world watched in merriment as they became irrelevant, even giving up on themselves at this year’s trade deadline.

Well, here are the Minnesota Twins, still standing, and looming as baseball’s greatest nightmare, threatening to devastate the TV ratings and marketing campaign.

The team that Major League Baseball and its former ownership couldn’t kill off is on Broadway, facing the powerful New York Yankees at 8 p.m. ET Tuesday (ESPN) in a winner-take-all American League wild-card game at Yankee Stadium.

If the Twins win and advance to play the Cleveland Indians, that screaming sound you’ll hear will be from the folks on Park Avenue and in the TV studios.

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“We’re kind of the red-headed stepchild,’’ Twins catcher Chris Gimenez tells USA TODAY Sports, “of everything that goes against playoff baseball. I was watching SportsCenter (Monday) morning, and it was ridiculous. It was like they were already giving the game to the Yankees.

“I know they’re a good team, and we got swept here 10 days ago, but that was 10 days ago. They’re a damn good team, and nearly won the AL East, so it’s not someone we take lightly. But they’d be smart not to take us lightly, either.’’

The marketing folks will tell you their affinity for the Yankees is nothing personal. The Twins are a lovable team. The clubhouse is filled with guys you want to emulate.

Yet, this is all about money, ratings, and marketing opportunities.

And the Twins are trying to ruin it all.

“That’s what we’re shooting for,’’ Twins second baseman Brian Dozier says. “We’ve been playing with a chip on our shoulder, and it’s been working.

“So why change now?’’

The Twins have already defied the greatest of odds. They’re the first team to lose 100 games — 103, more accurately — and reach the postseason the following year. They outscored the opposition by only 27 runs all season. They likely won’t have a single player finish in the top 10 of the MVP race, and had only three pitchers win more than seven games.

Why, even their own front office doubted their validity. Instead of trying to bolster their team at the trade deadline like every other contender, they actually dumped players. They sent All-Star closer Brandon Kintzler, who had 28 saves, to the Washington Nationals, just two days after trading veteran starter Jaime Garcia to the Yankees.

The Twins’ players were furious. Sure, they had lost 12 of their past 17 games, had dropped to five games back in the American League wild-card race, but there were still 59 games left in the season.

Twins manager Paul Molitor, whose contract expires at the year’s end, was just as upset as the players. He walked into the visiting clubhouse at Petco Park on Aug. 1, the day after Kintzler was traded, and wrote on the white board:

No retreat, no surrender.

The players took it from there, and gathered for a 10-minute meeting, led by veterans Joe Mauer, Matt Belisle and Dozier.

“Instead of getting down on ourselves,’’ center fielder Byron Buxton says, “we turned it into anger. Guys were angry. They still are. They were brothers to us.

“We told ourselves that we were going to leave everything on the field, every day. Whatever happens, happens. That allowed us to have a lot more fun instead of worrying about what we just lost.’’

The Twins promptly went 20-10 in August, and cruised to their first playoff berth since 2010, trying to win their first postseason game in 13 years.

“Everybody was angry when that happened,’’ Dozier said. “When they traded those guys, we got together, and it was like, ‘OK, screw it!’ We told guys, ‘If you find this motivates you, go with it. If you want to play with a chip on your shoulder, play with it.’

“Really, that’s been kind of our recipe to success, finding ways to motivate us.’’

Certainly, it wasn’t quite what Twins executive vice president Derek Falvey had in mind when he made the trades, but considering the effect it had on his team, maybe he could start an industry trend. You want to win, infuriate your players.

“It was a unique opportunity to grab some pitchers for the future,’’ Falvey said, “while balancing the present. I will say this: We had a lot of players on our club that were of interest to other clubs. We weren’t looking to tear this thing down.

“I certainly recognize there would be some feedback from the group that was not favorable, but I credit these guys. They have as been as resilient a group as I’ve seen.

“They bonded together, and said, ‘We don’t care what anybody else thinks of us, we’re going to push forward, and we’re going to give ourselves a chance to play tomorrow.’ ’’

Now, here they are, the biggest underdogs in this October baseball dance, not that anyone is giving them a shot to get past the Yankees.

This is a Yankee franchise that eliminated the Twins in the playoffs in 2003, 2004, 2009 and 2010. The Yankees have gone 89-33 against the Twins since 2002, winning the season series 15 consecutive years. And the Yankees have won nine consecutive playoff games against them.

“We play our best when our backs are against the wall,’’ Gimenez says, “and in a one-game playoff, on the road at Yankee Stadium, our backs can’t be any further back against the wall.

“Look at us. We’ve done a lot of things this year that have baffled people. So there’s no reason to stop now.’’

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Gallery: Five years of wild card games