NEW YORK -- As the longest-tenured player in the Yankees’ organization, Kyle Higashioka thought he knew what it would feel like to stroke a walk-off hit at Yankee Stadium. He’d experienced the rush of victory many times before, charging from the dugout to celebrate a teammate’s moment, yet never had that opportunity for himself.

As Higashioka bounded into second base with a game-winning double on Sunday, stamping a conclusion on the Yankees’ wild 4-3, 13-inning victory over the Brewers, he whirled to find Aaron Judge, Gleyber Torres and others already trying to rip his uniform jersey off, pummeling the catcher amidst a shower of sunflower seeds and gum.

• Every no-hit bid broken up in extra innings

“I was hoping they didn’t take everything off. Nobody needs to see that,” said Higashioka, in his seventh season with New York. “Just the support from the guys is a great feeling. Hopefully we come together and play well for the rest of the season. This last part of the season is a real revealer of character. You’ve got to grind through it and play your best, no matter what the circumstances are.”

And those circumstances, for most of Sunday afternoon, had been a combination of frustrating and odd. One by one, the Yankees spent most of their afternoon making hard right turns back toward their dugout, unable to figure out Corbin Burnes over eight hitless innings. Fortunately for the Yanks, Gerrit Cole matched Burnes with scoreless ball.

Milwaukee held the Yanks hitless through nine innings, then a 10th, as Sal Frelick and Joey Wiemer collided on Frelick’s sensational catch near the right-field wall that robbed Anthony Volpe of what could have been a game-winning hit, leaving Wiemer with a mouth full of blood.

• These 4 no-hitters required extra innings

Oswaldo Cabrera denied the Brewers what would have been the first 11-inning no-hitter in AL/NL history, ripping a game-tying run-scoring double with one out in the 11th. Just when the Yanks seemed sunk by a pair of 12th-inning runs, Giancarlo Stanton blasted a game-tying two-run homer into the Bombers’ bullpen, and on the game went -- until Higashioka delivered their sixth walk-off win of the year.

“We were no-hit for 10 innings, then we started chipping,” Cole said. “We started grabbing some momentum, so it was a cool combination of two narratives that culminated in a win.”

As Burnes held the bats quiet, limiting the Yanks to a pair of fifth-inning walks, Cole authored a piece of franchise history while burnishing his case for the American League Cy Young Award. Hurling seven strong innings of three-hit ball, Cole lowered his ERA to an AL-leading 2.79; his 23 starts of two runs or fewer are the most in the Majors.

Cole struck out nine, registering his 200th of the season with a punchout of Andruw Monasterio in the fifth inning, making him the first Yankee to record 200 or more strikeouts in three seasons.

“It’s a cool number,” Cole said. “I’ve got some more work to do. I’ve done it a few times, and it’s something I’m proud of. A lot of other people in this room have contributed. The ball leaves my hand, but a lot of the thoughts come from other people. I’m thankful I’m able to stay healthy and have people that surround me to support it.”

Said manager Aaron Boone: “I do that Immaculate Grid [game], and it’s amazing how many people don’t have 200 strikeouts, and you think they would. He’s got a lot of them.”

Long before he’d be summoned to come off the bench and catch the final four innings, Higashioka said that he parked himself next to special advisor Andy Pettitte in the tunnel between the dugout and the clubhouse. Together, the longest-tenured Yankee and the legacy Yankee marveled over Cole’s performance.

“We were just kind of laughing,” Higashioka said. “When you throw certain pitches, they’re so nasty. We knew that they didn’t have much of a chance against him today, with the stuff he had. It’s fun to watch.”

Considered a front-runner to notch his first career Cy Young Award after a pair of runner-up showings, Cole needs a strong September finish to hold off the Mariners’ Luis Castillo, the Blue Jays’ Kevin Gausman and the Twins’ Sonny Gray.

“Corbin was obviously on his game, very much so today, and he’s one of the best pitchers in the world,” Cole said. “As a fellow pitcher, you definitely respect that kind of effort. It was a well-pitched ballgame, and relatively quick, too, for it being 13 innings.”