NEW YORK — James Paxton and Chris Sale came out firing in this year’s first edition of baseball’s biggest rivalry.

Boston Red Sox right fielder Mookie Betts leaps for but can’t get to a solo home run by New York Yankees’ Clint Frazier during the fourth inning of a baseball game Tuesday, April 16, 2019, in New York. (AP Photo/Kathy Willens)

Paxton pumping 99 mph, and Sale nearing 98.

Only one of those hard-throwing lefties got results to match.

Paxton struck out 12 in his first pinstriped clash with Boston, Sale found his fastball but still got smacked around, and the New York Yankees three-hit the Red Sox 8-0 on Tuesday night in the first game this season between the struggling AL East foes.

Paxton (2-2) pitched two-hit ball for eight innings, walking one and going to just two three-ball counts in a swift game that took only 2 hours, 23 minutes.

“I felt like I was searching before this,” Paxton said. “I felt like I really found something tonight.”

Mike Tauchman hit his first major league homer and drove in four runs, and Clint Frazier and Gleyber Torres also went deep for the Yankees. New York had dropped five of six and is 7-9 a year after winning 100 games.

Sale (0-4) reached 97.5 mph — a positive sign for Boston after his velocity sagged this spring — but still allowed four runs and seven hits over five innings. He struck out six and walked one while the World Series champions dropped to 6-12.

“I stink right now,” Sale said. “I don’t know what it is.”

The longtime rivals hadn’t played with both teams below .500 this deep into a season since 1992.

Acquired from Seattle in an offseason trade, Paxton adjusted well after Yankees special adviser Carlos Beltran informed the left-hander he was tipping pitches during a lousy start last week in Houston. Yankees manager Aaron Boone also said before the game he thought Paxton’s stuff had dulled a bit since spring training.

Between starts, Paxton watched some old film of himself and tweaked his mechanics to match. It all clicked Tuesday. He drilled away with upper 90s fastballs, striking out four of his first six batters and six straight later.

“When I’m throwing that fastball like that, everything plays off of it,” Paxton said.

He saluted the cheering crowd after retiring AL MVP Mookie Betts to end his night.

“I think it’s a little bit different than anywhere else, being in Yankee Stadium and getting that ovation,” Paxton said.

Boston’s starters entered with a 7.18 ERA, worst in the majors, leading the club to bring up touted game-caller Sandy León from Triple-A and put him at catcher. Blake Swihart was designated for assignment.

Sale responded with some extra juice, just not enough. He entered with a 1.61 ERA in 17 games against the Yankees, best by any pitcher against New York since 1920, with a minimum of 75 innings.

“Throwing was better but still need to pitch better,” Sale said. “Got to get results.”

Frazier homered off the top of the right field wall to open the fourth. Betts nearly got a glove on it, but he came up short and got up slowly after slamming into the fence. He was still favoring his right wrist a couple of batters later but remained in the game. He said after that he was fine.

Tauchman doubled in a run later that inning, then hit a three-run drive in the sixth. The backup outfielder raised his batting average to .200 since being acquired at the end of spring training from the Rockies.

“As the new guy, you always want to help the team and do whatever you can,” Tauchman said. “It’s great to contribute to a really quality win.”

Xander Bogaerts doubled in the fourth for Boston’s first hit. The ball carried just over jumping right fielder Aaron Judge, bounced off the top of the wall and skipped back into play. Red Sox manager Alex Cora asked for a replay review, which upheld the two-base hit, putting runners at second and third.

The only other hit off Paxton was Jackie Bradley Jr.’s double in the eighth.

TRAINER’S ROOM —Red Sox: OF Andrew Benintendi was held out of the lineup with a bruised right foot. He fouled a ball off it Sunday. … Bradley was back in the lineup after sitting out Monday with the flu. … 2B Dustin Pedroia got a night off, which should be a regular occurrence this season in his return from a knee injury. … RHP Erasmo Ramirez was called up from Triple-A and allowed Tauchman’s homer.

Yankees: 1B Greg Bird was placed on the 10-day injured list before the game, giving New York a dozen players on the shelf less than three weeks into the season.

UP NEXT — Red Sox RHP Nathan Eovaldi (0-0, 8.40 ERA) faces Yankees LHP J.A. Happ (0-2, 8.76) in a matchup of impact 2018 trade acquisitions who are struggling this season.