CLEVELAND — When the the New York Yankees left Progressive Field last Friday night, they looked like a team on the verge of having its season end.

When the Yankees walked out of the same ballpark Wednesday night, they were smiling and headed to the airport for a flight to Houston and the American League Championship Series.

The Yankees finished their rally from a 2-0 deficit in the best-of-five American League Division Series with a 5-2 victory over the Cleveland Indians in Game 5 as shortstop Didi Gregorius hit a pair of home runs. The Yankees and Astros begin the ALCS on Friday night at Minute Maid Park.

That was quite a turn of events from five days earlier when the Yankees blew a five-run lead in Game 2 and lost 9-8 in 13 innings.

“There’s just a ton of fight in this club,” Yankees manager Joe Girardi said when asked how his club rallied to beat the Indians, whose 102-60 record in the regular season was the best in the AL. “It’s a great mixture of youth and veteran players that are the leading the way and it’s hard to believe because we just beat a really, really good team.”

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It was Gregorius, a young veteran, who set the tone by hitting a pair of home runs off Indians ace Corey Kluber to put the Yankees ahead 3-0. The 27-year-old hit a solo shot in the first inning and a two-run homer in the third off the favorite to win the AL Cy Young award.

Kluber was 18-4 with a 2.25 ERA in 29 regular-season starts. He led the AL in earned run average and tied for the league lead in victories.

The Indians scored a pair of runs in the fifth inning on back-to-back RBI singles by Roberto Perez and Giovanny Urshela, the bottom two hitters in the order, to draw within 3-2 and chase starter CC Sabathia.

However, David Robertson relieved and got Francisco Lindor to hit into an inning-ending double play — started by Gregorius — and the Indians never scored again. Robertson worked 2? innings for the win, and Aroldis Chapman pitched two innings for the save.

Meanwhile, Gregorius enjoyed the best moment of his six-year career. The Yankees acquired him from the Arizona Diamondbacks in a trade prior to the 2015 season and tasked him with replacing legend Derek Jeter at shortstop.

“As a kid, we always want to play in a big situation,” Gregorius said. “The first thing, you want to make it to the big leagues, watching everybody play in the big leagues, seeing all the players, awesome careers they’re having.

“Now I’m here, being in this unbelievable organization, all the history and everything that’s been here with this team, it’s just amazing to be in this situation.”

Kluber’s performance in the ALDS was amazing, though not in a good way. He was tagged for nine runs in 6? innings in his two starts after giving up just six runs total in his last six regular-season starts.

There had been speculation following Game 2 that Kluber was hampered by lower back soreness, and Indians manager Terry Francona confirmed it after the game. The same injury sidelined Kluber for almost the entire month of May.

“I think he’s fighting a lot of stuff, and I think you also have to respect that guy wants to go out there and he’s our horse,” Francona said. “Sometimes it doesn’t work.”

Things did not work out for Girardi in the Game 2 loss, and that led to speculation he might be fired if the Yankees lost the series.

The Yankees seemed to have that game in hand, leading 8-3 with two outs in the bottom of the sixth inning when home plate umpire Dan Iassogna ruled that the Indians’ Lonnie Chisenhall was hit by a Chad Green pitch to load the bases.

Television replays appeared to show the ball hit the knob of Chisenhall’s bat and into catcher Gary Sanchez for what should have an inning-ending strikeout. However, Girardi did not challenge the call and Lindor followed with a grand slam to draw the Indians within a run.

The Indians tied in at 8-all on Jay Bruce’s home run in the eighth inning and won it on Yan Gomes’ RBI single in the 13th.

However, the Yankees then won three games in a row to take Girardi off the hook and advance to the ALCS.

“I was about as low as I could be as a baseball (person),” Girardi said. “I’ve been carrying this burden for five or six days. It’s hard. If we lose on Sunday, it really hurt. If we lose on Monday, it really, really hurts. If we would have lost (Wednesday night), it probably would have hurt even worse.

“So, for me, what those guys did for me, I’ll never forget it.”

Follow John Perrotto on Twitter @JPerrotto.