KANSAS CITY, Mo. — The Yankees finally received the game they were waiting for from Aaron Judge. Just, it was not from Aaron Judge.

It was from the original mammoth, “I can’t believe how hard and far he just hit that ball” edition. Because as Judge continues to try to figure out how to rise in this month, Giancarlo Stanton is showing — regardless of the lengthy injury history and extended slumps he can experience from April through September — there is some Mr. October in him.

“This is what I came here for,” Stanton explained about why he delivers at this time of year.

Judge had better at-bats in Wednesday’s Game 3. He smashed a first-inning liner 114.4 mph that had an .860 expected batting average, but Royals shortstop Bobby Witt Jr. caught it with a leap. Judge just missed a ball that nevertheless soared to deep left. He should have walked in the seventh, but a check swing that wasn’t a swing was called a strike. And he did walk in the ninth.

Ultimately, though, Judge is still 1-for-11 in this series and batting .203 in 47 career playoff games. Plus, he was part of a top four in the lineup — with Gleyber Torres, Juan Soto and Austin Wells — that went 0-for-15.

It further burdened the No. 5 hitter. Stanton responded with a 114.1 mph RBI double in the fourth. He singled and — really, don’t go for an eye exam — stole a base in the sixth. And with a tie score and one out in the eighth, he crushed a Kris Bubic slider 417 feet.

That was the difference in a 3-2 Yankees victory over the Royals that pushes them within a win of advancing to the ALCS.

“From his first at-bat to his last at-bat, I could tell how locked in he was,” Jazz Chisholm Jr. said.

Stanton actually began to lock in long before his first at-bat. In an empty stadium, Stanton came out alone to take extra work off a machine that can deliver MLB-style fastballs and sliders, something hitting coach James Rowson said he likes to do on occasion. Stanton said he wanted to get a good feel for the hitting background at Kauffman Stadium and also practice spraying it around the yard.

“I am telling you, one of the biggest things that hit me working with [Stanton] this first year, from the beginning, is seeing just how much he cares,” Rowson said.

Stanton, with an MVP and a $300 million-plus contract and (at minimum) an outside chance at 500 homers, has nevertheless been relegated this season with so much attention on the Soto-Judge duo. Plus, Stanton served more IL time and looked like an elderly jogger at times, as he protected his oft-injured legs while running the bases.

What remained the same was that when his bat squared on the ball it traveled at speeds and distances perhaps only Judge can truly comprehend.

And now he is back in his time of year. Stanton has a .964 OPS and 12 homers in 30 playoff games.

“He’s so good at locking in in these big games,” Aaron Boone said. “He’s done it throughout his career with us. He’s just really able to focus from pitch to pitch. I thought that at-bat off Bubic was just phenomenal. I think he went up there looking to do damage, looking to do just that.”

The implication of that swing was large. The Royals had spent most of this series outplaying the Yankees. The best-of-five was tied both 1-1 in games and 2-2 in the eighth inning of Game 3. The Yanks were teetering toward making it 4-for-4 of the higher seeds in the Division Series going down 1-2. And that would put the Yankees a loss away from explaining yet more October failure.

But they overcame. It sure seemed Torres had dumped a hit that struck the right-field foul line that should have put two on with two outs in the third inning. But an actual right-field umpire missed it and the replay center upheld it with what looked like unclear, obstructed replays that made your family’s old home videos play like Spielberg.

Chisholm, for the offense of calling the Royals “lucky” after a Kansas City Game 2 win in The Bronx, was booed like someone who took an illegal hit or two on Patrick Mahomes, a minority Royals owner who was at Game 3.

The Yanks actually had many good at-bats — Anthony Volpe and Oswaldo Cabrera, particularly — and a successful sac bunt from Alex Verdugo and the shocking steal from Stanton. But they were 1-for-13 with men on base, reconfirming that when they do not hit the ball out of the park, these Yankees simply have trouble scoring.

So Stanton hit it out of the park.

“You come into the game understanding that,” Stanton said of understanding the swing between being up 2-1 or down 1-2. “And then I’ve just got to focus, laser focus on the at-bat, and good things will happen from there.”

Good things happened, again, in October for Stanton. He’s been here before and excelled. So when he meets the moment — and the ball with ferocity — you know it is not one thing:

Lucky.