NEW YORK -- Houston, here come the Yankees.

Riding a strong start from lefty Nestor Cortes, the New York Yankees booked a ticket to the American League Championship Series with a 5-1 victory over the Cleveland Guardians on Tuesday. The Game 5 victory capped a back-and-forth series in which the Yankees faced elimination in Game 4 in Cleveland and rain delayed multiple contests.

New York now faces off against the Astros in a best-of-seven series that starts in Houston on Wednesday when Justin Verlander and Jameson Taillon go head-to-head in Game 1. During the regular season, the Astros and Yankees finished with the two best records in the American League, respectively, while Houston took five of seven games against New York.

Giancarlo Stanton put the first runs on the scoreboard in the first inning Tuesday, hitting a line-drive home run on an 87.5 mph cutter from Cleveland starter Aaron Civale over the right field wall, scoring Gleyber Torres and Anthony Rizzo and putting the Yankees on top 3-0. Civale lasted one more batter, throwing just 26 pitches and recording a single out before Guardians manager Terry Francona gave him the hook.

Aaron Judge tagged on another run in the second inning, hitting an 81.3 mph curveball from Sam Hentges over the right-center field wall to make it 4-0. It was Judge's fourth homer in a winner-take-all game -- the most in major league history -- and the 13th homer for the towering slugger in his postseason career, catapulting him past Reggie Jackson and Yogi Berra for the fifth-most in Yankees postseason history.

The Yankees faced a scary moment in the third inning when shortstop Oswaldo Cabrera collided with outfielder Aaron Hicks on a bloop popup to left field off the bat of Cleveland outfielder Steven Kwan. Hicks left the game with a left knee injury and underwent an MRI at New York Presbyterian. He will miss the remainder of the postseason.

Cleveland struck back with its only run of the game later in the third inning when third baseman Jose Ramirez hit a sacrifice fly to center fielder Harrison Bader, scoring Austin Hedges to make the score 4-1. The run proved to be the only offense the Guardians generated in their final game of the season, tallying eight hits while leaving six runners on base and going 0-for-6 with runners in scoring position.

Rizzo tagged on another run for the Yankees in the fifth inning with an RBI single to center off Guardians reliever James Karinchak to drive in Torres, who stole second base to move into scoring position after drawing a walk.

Cortes left the game after the fifth inning after throwing 61 pitches, allowing just three hits, one run and one walk while striking out two batters. He was working off of just three four days of rest, last pitching on Friday in Game 2. Throughout the outing, Cortes used a mix of his fastball (54%), cutter (26%) and slider (16%).

The departure of Cortes handed the keys to the Yankees' fate to the bullpen, which appeared to be the team's biggest weak spot heading into the postseason. First, Boone called upon Jonathan Loaisiga, who allowed singles to Amed Rosario and Ramirez before getting Oscar Gonzalez and Josh Naylor to ground out. He then struck out Gabriel Arias to end the sixth. Loaisiga returned for another inning and finished off the seventh, ending the evening with two innings pitched, allowing three hits and no runs or walks while striking out two.

Clay Holmes entered in the eighth inning and shut down the top of the Guardians' order, striking out Rosario and Gonzalez and inducing a groundout from Ramirez.

Holmes then handed the ball off to Wandy Peralta, who became one of Boone's go-to relievers during the series, pitching in every game. Peralta got Naylor to ground out before allowing a single to Arias, striking out Andres Gimenez and allowing a single to Luke Maile. With two runners on, Peralta got Myles Straw to ground into a fielder's choice and punched New York's ticket for a matchup against the Astros.

The Yankees and Astros face off in Houston in Game 1 of the ALCS on Wednesday starting at 7:37 p.m. ET.