NEW YORK -- Chad Green reared back and dotted the top of the strike zone, a heater that Jonathan Villar waved at. The Yankees reliever pounded his right fist into his glove, perhaps not realizing that he’d just completed an immaculate inning, but well aware that it had been an important performance.

Following an afternoon in which the Yankees blew a late lead and weathered one of their most deflating defeats of the season, Green helped restore order. The right-hander’s three perfect innings sealed a 4-2 victory over the Mets, as the Yanks took the nightcap of Sunday’s Subway Series seven-inning doubleheader at Yankee Stadium.

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“We’ve had some pretty devastating losses the past few games, games we should have won that we just weren’t able to get done,” Green said. “I think that was a very important game for us.”

With fireworks echoing around the South Bronx, Green struck out Michael Conforto, pinch-hitter Jeff McNeil and Villar on nine pitches in the breezy seventh. According to STATS, Green became the first pitcher in the Modern Era (since 1900) to pitch three perfect innings, strike out six batters and have an immaculate inning in the same game.

“He had terrific command, throwing the ball how and where he wanted to,” Yankees manager Aaron Boone said. “I was a little reluctant to send him out there for a third inning, but he wanted the ball. He was dominant and efficient. That was just a huge effort for us.”

Green tossed two pitches in Game 1 of the twin bill, before yielding to closer Aroldis Chapman, who blew a save opportunity in a 10-5 loss that saw the Mets bat around for six seventh-inning runs. The Yankees bounced back, as Gio Urshela slugged an opposite-field three-run blast off Corey Oswalt that provided most of their offensive production, supporting a strong spot start by Nestor Cortes Jr.

Described by Boone as someone who “pitches without fear,” Cortes’ funky, unpredictable delivery kept the Mets guessing into the fourth inning.

“This was huge,” said Cortes, who struck out four in 3 1/3 frames of one-run ball. “We had to come out and salvage this series. It’s super important that we got the job done.”

Dominic Smith chased Cortes with a one-out double in the fourth, and Pete Alonso greeted Darren O’Day with a two-run homer, his second long ball of the doubleheader. But O’Day escaped without further damage. Brett Gardner dashed home on a fifth-inning wild pitch for an important insurance run.

Boone explained that he preferred Chapman in the Game 1 save situation because he believed Green would be needed for length, a blueprint that worked perfectly. The Mets did not get a ball out of the infield against Green, who could be considered as a fill-in closer while Chapman tries to figure out his ongoing issues with fastball command.

"Chad Green did an amazing job,” Mets manager Luis Rojas said. “That guy pitching both games, that's something special. That doesn't happen often now in baseball."

Happy Fourth of Gio-ly
After the Yankees were kept in the ballpark in Game 1, Urshela’s second-inning homer provided all of the offense they needed in the nightcap. Luke Voit started the frame with a towering double to left-center field and Rougned Odor legged out a bunt single to bring up Urshela, who said that he was thinking about a sacrifice fly in that at-bat against Oswalt.

Instead, Urshela hacked at an up-and-away fastball out of the strike zone and punched a drive 346 feet to right field -- a blast that would have been a homer in only three Major League parks (New York, Houston and Seattle). Of Urshela’s last 14 home runs, 10 have either tied the game or given the Yankees a lead.

“That was a really high pitch, but thank God I got it on the barrel,” Urshela said. “When I hit it, I felt like I hit it good. I thought it had to at least be a flyout so the run could score, but it got out.”

Jet set
Sunday’s doubleheader split concluded an eventful homestand for the Yankees, one that featured strong words from managing general partner Hal Steinbrenner and general manager Brian Cashman, as well as a players-only meeting called by Aaron Judge before a June 29 victory over the Angels.

Having dropped four of six games in The Bronx -- as well as seven of their past nine coming off a series sweep by the Red Sox at Fenway Park -- Boone believes that his 42-41 club has a tall task ahead as it flies West for series against the Mariners and Astros leading into the All-Star break.

“We understand what’s at stake, and I think we understand the hole we’ve dug for ourselves,” Boone said. “We’re going out west with a lot on the line.”