Yankees starter James Paxton pitches during the first inning of...

Yankees starter James Paxton pitches during the first inning of a game against the Boston Red Sox in Boston on Monday. Credit: AP/Michael Dwyer

BOSTON — James Paxton suddenly looks like the least of the Yankees’ concerns when it comes to their postseason rotation.

The lefthander, the prized acquisition of GM Brian Cashman last winter who spent much of his first season in the Bronx struggling to find consistency, won his eighth straight game Tuesday night in a 5-0 victory over the Red Sox in front of 35,884 at Fenway Park, a crowd that saw the hometown team officially eliminated from AL East contention.

Paxton, now 13-6 with a 3.96 ERA, including 8-0 with a 2.57 ERA in his last eight starts, allowed four hits and three walks over 6 2/3 scoreless innings in which he struck out seven.

“Best pitcher in the game with the type of stuff he has, his arsenal,” said Aaron Judge, who went 2-for-4 with a double. “He’s getting right at the right time.”

The Yankees (95-50), keeping pace with the Astros for the Majors’ best record, finished the season 14-5 vs. the reeling Red Sox (76-68), who stunningly fired their president of baseball operations, Dave Dombrowski, late Sunday night.

It marked the most victories for the franchise against the Red Sox since going 15-7 in 1960. Afterward, Frank Sinatra's “New York, New York” pulsated through the clubhouse walls — a song that created a silly non-story during last season’s ALDS when Judge blasted it walking of Fenway after a victory in Game 2 (the Red Sox played it in their clubhouse after eliminating the Yankees and then after topping the Dodgers in the World Series). 

“It’s a good song,” Austin Romine said with a smile about a song rarely if ever heard on the clubhouse playlist after a win.

Judge insisted there was no significance to going 14-5 against the Red Sox this season after being eliminated by them in 2018. 

“Not really,” he said. “We’ve got the better team. We just want to go out there and play our game. We knew that from the beginning.”

Paxton, meanwhile, was coming off a start last Tuesday vs. the Rangers when he allowed one hit, and struck out 12, over seven scoreless innings. The start before that, Aug. 28 at Seattle, the 30-year-old allowed one hit and two runs over five innings and the start before that he struck out 11 at the Dodgers while allowing two runs and five hits.

“I feel great about the spot that I’m in right now, how I’m throwing the baseball,” Paxton said. “Just want to stay there and go into the postseason feeling this way.”

Monday night Paxton was backed by and offense that didn’t do a ton but still got homers from Austin Romine and Gio Urshela, yet another hit by DJ LeMahieu with a runner in scoring position, a sacrifice fly by Gleyber Torres and a ninth-inning RBI single by Luke Voit that made it 5-0.

Boston lefthander Eduardo Rodriguez, 17-5 with 3.81 ERA coming in, pitched well, but not quite good enough. He allowed one run — coming on Romine’s homer in the fifth that made it 1-0 — and five hits over six innings in which he walked one and struck out nine.

Paxton, who brought a 9.72 first-inning ERA into the night, made it four straight outings in which he did not allow a first-inning run.

“He’s in a really good place,” Aaron Boone said of Paxton. “Obviously, it’s coming down to the wire down the stretch, and we hope to have a lot of baseball left, but you certainly like to see guys at their best this time of year, no question.”

Urshela’s homer, his 19th, off lefty Darwinzon Hernandez kicked off a three-run seventh that included LeMahieu’s RBI single that made him 46-for-115 (. 400) with RISP this season and Torres’ sac fly.

“We feel really confident as a team right now,” Paxton said. “And it feels great to knock those guys out, of the division anyway. We’re just going to keep on going forward and get ready for the postseason.”

More Yankees headlines