One Yankee after another smothered James Paxton with praise from the home clubhouse. Down the hall, Mookie Betts and Alex Cora added hosannas after the left-hander overpowered the Red Sox on Tuesday night.

In a matchup of blood rivals desperate for a win that could possibly deliver life after nightmarish starts to the season by each side, Paxton proved to be far too much for the defending World Series champions.

Working with a fastball that almost made triple digits from the first inning and backed by home runs from Clint Frazier, Mike Tauchman and Gleyber Torres, Paxton hurled the Yankees to an 8-0 victory in front of 45,008 apathetic Yankee Stadium customers.

“It’s a big deal against Boston. We want to beat Boston every time,’’ said Paxton (2-2), who allowed two hits, walked one and fanned a dozen in eight innings in his first taste of Red Sox-Yankees.

When catcher Austin Romine checked the speed gun readings high above the jumbo screen in center field and saw 97 mph and 98 mph, he felt there was something special to the 30-year-old lefty.

“He established the fastball and made his off-speed [stuff] better,’’ Romine said. “Too much to cover the rest of the plate.’’

Paxton easily retired the first nine Red Sox before walking Betts to start the fourth while protecting a 2-0 lead. Xander Bogaerts followed with a double to right that gave the visitors runners at second and third and no outs. Paxton responded by retiring J.D. Martinez and Steve Pearce on fly balls to right — neither deep enough to score Betts — and stranded two by striking out Mitch Moreland on a 2-2 pitch.

That punch out was punctuated by Paxton slamming his left hand into his glove as he walked off the mound.

“I felt like it was a big part of the game,’’ said Paxton, who is 3-0 with a 1.89 ERA in five career starts against the Red Sox. “We were ahead of them, but I didn’t want to let them back into the game.’’

That 2-0 cushion, which was provided by RBI singles from DJ LeMahieu and Luke Voit in the third, stretched to 4-0 in the fourth when Frazier led off with a homer against Chris Sale and Tauchman doubled home Romine from first. Tauchman’s first big league homer off Erasmo Ramirez reached the upper deck in right and scored three in the sixth for a 7-0 advantage. Torres opened the seventh with his fourth homer that accounted for the final run.

“We were ready to go from the first inning,’’ Aaron Judge said of the lineup that produced at least one hit from every spot. “Quality at-bats up and down the lineup.’’

Sale opened the night with a 6-4 career record and a 1.61 ERA in 17 games (14 starts) against the Yankees. Though his velocity was up from his previous three starts, it wasn’t enough to stop the Yankees. In five innings, Sale (0-4) gave up four runs, seven hits, walked one and fanned six.

“Hats off to [Paxton], he set the table for us. In the first inning he showed what he had,’’ Judge said.

What the Red Sox saw was a dominant hurler on top of his game.

“Throwing a lot of strikes, keep it out of the middle of the plate. He’s got good life on his fastball. He pitched an amazing game,’’ said Betts, who was called out leading off the game on a 97-mph fastball.

Cora, the Red Sox manager, noticed a lot more life on Paxton’s fastball than he had seen looking at tape of the lefty’s last start against the Astros.

“Velocity was way up. He barely used his breaking ball the first part of the game,’’ Cora said. “We had second and third and didn’t score. From there he took off. He used his fastball a lot, in and out, up. We weren’t able to catch up with it.’’

— Additional reporting by Ken Davidoff