SAN DIEGO — The New York Yankees signed the man they desperately desired last winter.

He pitched just the way they envisioned all season-long.

Now, the Yankees are leaning on Gerrit Cole to pitch the biggest game of their season Friday in a winner-take-all game with the Tampa Bay Rays, and asking him to perform on short rest for the first time in his career.

The dream scenario came to realization when the Yankees knocked off the Tampa Bay Rays, 5-1, Thursday night, setting up the deciding Game 5 at Petco Park for the right to play the Houston Astros in the American League Championship Series.

Cole vs. Rays’ Tyler Glasnow, Game 2 starter.

“Well, this is a team that has been through a lot of pressure,’’ Yankees manager Aaron Boone said. “2020 brought pressure beyond what any of us could fathom.

“Pressure is a privilege. Major League athletes, you have to embrace that. I think our guys overwhelming do.’’

Well, the Yankees sure seemed to embrace it Thursday, relying on Jordan Montgomery to deliver his biggest start of the season, with five shutout innings from the rest of the bullpen, setting the stage for Cole, their $324 million man.

The Yankees planned all along this series that Cole would pitch Game 5, and although this will be Cole’s first start on short rest, he had only one message to Boone:

“Give me the ball.’’

The unsung hero of the night for the Yankees was Montgomery, who hadn’t pitched in two weeks, and was terrorized the last time he faced the Rays. Who would have imagined that he’d be the only one this entire postseason to shut down Randy Arozarena, the hottest pitcher on the planet?

Arozarena, who entered the game hitting .600 this postseason, and said earlier in the day that his favorite player is well, himself, went hitless in four at-bats, failing to hit the ball out of the infield.

Montgomery, who couldn’t get out of the first inning the last time he faced the Rays, surrendering five consecutive hits to open that game, just gave up one run in four innings on this night. He escaped a two-on, two-out jam in the third inning when Arozarena struck out, and again in the fourth inning, when Kevin Kiermaier ground out.

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It was more than Boone could have possibly hoped for, allowing him to turn to his bullpen in the fifth inning, starting with Chad Green, turning to Zack Britton in the 7th, and closer Aroldis Chapman for the final four outs.

The Yankees, if nothing else, proved they can at least win games without an offensive onslaught, relying on homers by Luke Voit and Gleyber Torres.

“It’s not easy to score runs, even when you have a great offense,’’ Boone said. “‘But when things are going well, we feel like we have the best offense in the game.’’

The Yankees are trying to win their 28th World Series, and their first since 2009. The Rays are looking for their first in franchise history.

 “I hope they enjoy the opportunity to play baseball,’’ Boone said, “and compete for something so meaningful in this wild and trying year.’’

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