BOSTON — For the second straight night, Aaron Judge absolutely obliterated a baseball at Fenway Park, sending a first-inning solo shot — his 37th of the season — over everything in left field and onto Landsdowne Street.

• Yankees land Chisholm from Marlins for 3 prospects

The first-inning spark set the tone for a wild one between the division rivals, as the Yankees scored a run apiece in the eighth and ninth innings to tie the game before winning it, 11-8, in 10 innings, snapping a three-game losing streak in the process.

“The fight from this group right now, while we’re going through it, we’re fighting for our lives right now,” manager Aaron Boone said after the victory. “The compete is so good; it was so good last night. Obviously, tonight got turned upside down pretty early, and you’re trying to piece it together. … Everyone kept picking it up.”

“A win’s a win, just like a loss is a loss,” said Judge with a smile. “We battled in [Friday’s] game, but you know, we lost that game. But we came out today ready to do our thing. You have to have tough moments, go through tough losses, but we came out with a win today.”

On Friday night, the Yankees’ slugger hit one of the most impressive shots of the year, a Statcast-projected 470-foot blast to the deepest part of center field at the Red Sox’s home ballpark. Saturday night’s shot went sailing over the Green Monster and was swatted a projected 432 feet. Per Statcast, the ball was hit with an exit velocity of 110.6 mph.

Taking the second pitch he saw out of the ballpark, Judge gave the Yankees a 3-0 lead as he followed a Juan Soto two-run blast into the Red Sox’s bullpen. It was the fifth time this season that the Yankees have gone back to back, the third by Soto and Judge.

It was also the fifth home run in the past 11 games for Judge, who leads all of baseball with his 37 dingers this season. He drove in another run in the fifth inning with a one-out single that tied the game at 5-5.

The Yankees coughed up their early three-run lead almost immediately, and the clubs battled back and forth, combining for 29 hits and six home runs.

Judge finished 4-for-4 with two walks, three RBIs (giving him a Majors-high 95 this season) and three runs scored as he raised his batting average to .314, third best in the American League. It was the first time in his career that he reached base six times in a game and the 10th time he produced four hits, his career high.

“It’s remarkable,” said Boone. “It’s really impressive what him and Juan are doing in that back-to-back in the order. You get to witness greatness every day. Six times on, it’s not an easy thing to accomplish.”

“He shows every night that he’s one of the best in the game right now,” added Gleyber Torres, who came up with a clutch two-run double in the 10th.

Judge nearly tied the game in the top of the eighth inning when he ripped a double off the wall in left field, but after Alex Verdugo scored from second, Soto ran through the stop sign at third base and was thrown out at home.

New York then found itself down to its last strike in the ninth inning before Trent Grisham delivered an RBI double off Red Sox closer Kenley Jansen to tie the game at 8-8 and send it to extra innings.

“I’ve seen him before a couple of times,” Grisham said. “So I tried to stay relaxed, stay comfortable and stay with my approach.”

“It’s fun,” noted Judge. “When you come to Fenway, the place is rocking from the very first pitch all the way to the last pitch, even down to our last strike when Grish was battling Jansen. These are the games you want to play in.”