After nearly becoming the first team in MLB history to get no-hit for 11 innings, the Yankees’ offense finally came alive and beat the Brewers, 4-3, in 13 innings on Sunday.

Kyle Higashioka won it with the first walk-off hit of his career — a double that scored added runner Everson Pereira — which finally ended what started off as a pitchers’ duel between Gerrit Cole and Corbin Burnes and turned into a back-and-forth game that ended the Yankees’ three-game losing streak.

“We were no-hit for 10 innings and then we started chipping and then we came back and started grabbing some momentum,’’ Cole said. “It was a cool combination of two narratives that ended in a win for us.”

Oswaldo Cabrera finally gave the Yankees their first hit — and run — with one out in the bottom of the 11th to tie the game.

And after Nick Ramirez gave up a pair of runs in the top of the 12th, Giancarlo Stanton tied it again with a leadoff two-run homer, driving in added runner Gleyber Torres.

After getting a scoreless inning from just-recalled Anthony Misiewicz in the top of the 13th, Higashioka won it.

“To me, personally, it means the world,’’ said Higashioka, who was mobbed by his teammates at second base. “It’s something every player goes for. But I think the more important thing is we gave ourselves a chance to win. We faced a tough pitcher early and we still didn’t give up. We just battled through it and grinded out a win.”

They also got another gem from Cole, who moved closer to winning his first Cy Young award with seven shutout innings. Cole lowered his AL-leading ERA to 2.79.

Burnes was even better, as he tossed eight no-hit innings before being removed after 109 pitches, one shy of his season-high.

Burnes was replaced by Devin Williams, who pitched the ninth, and Abner Uribe the 10th.

Against Joel Payamps in the 11th, added runner Anthony Volpe — who nearly won the game for the Yankees in the 10th with a shot to the wall in right — moved to third on an Everson Pereira groundout before Cabrera ripped a double to right.

After Higashioka whiffed, DJ LeMahieu walked and the Brewers intentionally walked Aaron Judge to load the bases for Gleyber Torres, who grounded out to get the game to the 12th.

Burnes retired the first dozen batters he faced before he walked Stanton to start the bottom of the fifth.

Stanton walked again with one out in the 10th and with Judge, the added runner, at second, Volpe sent a long fly ball to the wall in right-center, where Sal Frelick made a terrific, game-saving catch, as he collided with center fielder Joey Wiemer.

Cole and Burnes remained locked in a high-level pitchers’ duel throughout the afternoon, as Cole also became the first Yankee to reach the 200-strikeout milestone in three different seasons with his strikeout of Andruw Monasterio in the fifth.