NEW YORK -- It took about 15 minutes for one big swing by Giancarlo Stanton to erase any of the tension in the stands about the New York Yankees being in a winner-take-all postseason game.

A few hours later, there was a modest celebration inside the clubhouse before the Yankees headed to the airport for another postseason encounter with the Houston Astros.

Giancarlo Stanton blasted a three-run home run in the first inning, Aaron Judge followed with a solo drive an inning later and the Yankees beat the Cleveland Guardians 5-1 in Game 5 of the American League Division Series on Wednesday.

The Yankees overcame a 2-1 deficit in a best-of-five series for the third time -- and the second time against Cleveland. They advance to their third AL Championship Series meeting with the Astros, who have been off since beating the Seattle Mariners in 18 innings on Saturday. Game 1 is Wednesday night in Houston.

"We'll walk in there with some confidence," New York manager Aaron Boone said. "We know they are a great team and rested and ready. We look forward to the challenge."

After a 2 1/2-hour rain delay on Monday led to the second rainout of the series, the Yankees took the lead early in the Tuesday game and never looked back. They wound up having a celebration that featured loud rap music inside the clubhouse, some Champagne and a team picture on the field.

Stanton homered four batters in after Gleyber Torres opened with a walk and Anthony Rizzo was hit by a pitch with one out. Stanton hit his second homer of the series when he blasted a 2-0 cutter from Aaron Civale (0-1) into the right-center-field seats.

"We definitely had to throw the first punch in a game like this," Stanton said. "I was up with runners in scoring position. Tried to make sure I got a good pitch to hit and make sure I didn't roll into a double play. So get the ball in the air and it worked out.

Upon connecting, Stanton held his bat halfway down the first base line, yelled into his own dugout and dropped the bat before completing his trot.

Judge homered in the second against Sam Hentges when he sent a 1-0 curveball 394 feet to right-center. It was his major-league-record fourth homer in a winner-take-all game, and the Yankees improved to 28-2 in the regular season and postseason when Judge and Stanton homer in the same game.

"When you hit in the middle of the order, you got to come up big," Judge said. "Stanton, Rizzo (have) been doing it all series. I tried to step in there and do it when I can."

Rizzo added an RBI single in the fifth inning for the Yankees, who advanced to their 18th ALCS and third in six seasons.

New York's pitching plans also worked out well. The Yankees were initially slated to start Jameson Taillon on Monday, but after the rainout, they turned to Nestor Cortes on three days' rest.

Cortes (1-0) allowed one run on three hits in five innings. He walked one, struck out two and threw 61 pitches.

"Just the legend of Nestor," Boone said. "Physically I felt like he was good. Had we played last night, he would have played an important role for us."

Cortes became the sixth Yankee starting pitcher to toss at least five innings and allow one run or fewer in a winner-take-all game and the first to do it in New York since CC Sabathia pitched a complete game in Game 5 of the 2012 ALDS against the Baltimore Orioles.

"It feels incredible to be able to do what I did today," Cortes said.

The New York bullpen then took over. Jonathan Loaisiga stranded three over two innings, Clay Holmes tossed a 1-2-3 eighth and Wandy Peralta finished up the ninth as Gerrit Cole warmed up. The Guardians put two on in the ninth before Peralta got Myles Straw to ground into a game-ending force play.

Cleveland opted against using ace Shane Bieber on short rest, saving him for a possible relief appearance or a Game 1 start in the ALCS.

Civale got only one out and allowed three runs on two hits, one walk and one hit batter. He was lifted after Josh Donaldson reached on an infield single.

"I felt terrible taking him out that quickly, but I just didn't think we could give up any more," Cleveland manager Terry Francona said.

Jose Ramirez hit a sacrifice fly in the third for the Guardians, who dropped to 1-8 in winner-take-all games. Cleveland has lost eight straight winner-take-all contests since winning Game 5 of the 1997 ALDS against the Yankees.

"I know they are hurting right now because they care and they worked unbelievably hard," Francona said. "But I hope as that wears off, they will realize just how proud we are of them and how much we care about them."

--Larry Fleisher, Field Level Media