Gerrit Cole could never have anticipated the twists and turns of his first season with the Yankees, but this brand of challenge was exactly what the ace envisioned when he slipped on a pinstriped jersey for the first time and remarked that “pressure is a privilege.”

Saying that he loved the stakes of a heavyweight pitching matchup, Cole bested Shane Bieber, the American League’s likely Cy Young Award winner. Backed by some old-school thump, Cole and the Yankees defeated the Indians, 12-3, in Game 1 of the AL Wild Card Series on Tuesday evening at Progressive Field.

“We needed to set the tone for the series,” Cole said. “I’m very thankful and humbled to be able to take the ball and to be in this position. To be able to deliver feels really good.”

• Box score

Mixing his four-pitch arsenal with aplomb, the 30-year-old right-hander struck out 13, the most by a pitcher in his Yankees playoff debut. Cole walked none and became the first Major Leaguer to record three postseason games of 12 or more strikeouts.

Only Roger Clemens has fanned more batters in a Yankees postseason start, “The Rocket” having registered 15 strikeouts in Game 4 of the 2000 AL Championship Series against the Mariners. Cole joined Tom Seaver (1973) as the only pitchers to strike out 13 or more in a postseason start without a walk.

“This was a really good way to start out a series, against a good team and a great pitcher,” Yankees manager Aaron Boone said. “To have Gerrit throw the ball the way he did, that’s big. Now we’ve got to go do it again.”

Continuing an excellent five-start pairing with backup catcher Kyle Higashioka, Cole scattered six hits over seven innings, touched only by José Ramírez’s RBI double in the third inning and Josh Naylor’s solo homer in the fourth.

Otherwise, Cole was magnificent, showcasing the talent that spurred the Yankees to invest nine years and $324 million in his gifted right arm this past December.

“This is why we got him,” said Aaron Judge, who cracked Bieber’s fourth pitch for a two-run homer, staking Cole to a near-instant lead with the first of four Yankees home runs. “We didn’t get him to throw in April. We got him to throw in postseason baseball for the Yankees. He took it up another notch. He’s got that type of intensity, just being an animal out there.”

• Judge's blast sets tone for Yankees' outburst

Though Cole imagined his Yanks postseason debut would have come in a lively, bunting-strewn ballpark, he was buoyed by the knowledge that he had two friendly faces watching from a right-field suite -- his wife, Amy, and the couple’s 3-month-old son, Caden.

“I spent some time with him today in between naps,” Cole said. “This is the first time we got to go to the ballpark together as a family, so it’s something that I’ll always remember. I never thought that his first game would be in Cleveland.”

With Mom and baby observing from high above, Cole generated 12 swings and misses with an electric four-seam fastball that he dialed up to 98.8 mph to strike out Carlos Santana to end the third inning.

Cole challenged hitters with that heater, using it 55 times out of 105 pitches, while keeping the Tribe off-balance with his knuckle curve (25), slider (17) and changeup (eight).

“I thought he looked sharp,” Boone said. “He had all four pitches mixed in and he leaned on all of them. He just made a lot of big pitches to keep his pitch count down and polish off an impressive night.”

Luke Voit ripped a run-scoring double in the third inning. Brett Gardner and DJ LeMahieu collected fourth-inning RBIs.

• Gardy rewards Boone's faith with big night

Gleyber Torres chased Bieber when his two-run homer clanged into the left-field bleachers in the fifth, part of a four-hit, three-RBI performance for the infielder.

“We kept our foot relatively on the gas the whole night,” Cole said.

That healthy advantage allowed Cole to cruise, retiring eight consecutive batters after Naylor’s homer and 11 of the last 12 Indians he faced. Cole yielded to Luis Cessa for the final six outs, having improved to 7-4 with a 2.60 ERA in 11 postseason starts.

“It was definitely a special night, but especially in this year, we have a lot more baseball to go win,” Cole said. “We’ll celebrate the good stuff, shower it off and come back tomorrow to get after it.”