NEW YORK — Brock Holt had one thing in mind: He was swinging for the fences.

After all, the game was decided long ago. And everything else went Boston’s way all night, so why not this?

The part-time utilityman put the finishing touch on a Red Sox blowout, becoming the first player to hit for the cycle in a postseason game as Boston routed the New York Yankees 16-1 on Monday to seize a 2-1 lead in their best-of-five AL Division Series.

“This one I’ll remember for a long time,” said Holt, unaware of his achievement until told by a television reporter right after the final out. “Obviously, you don’t go into the game expecting to make history or do anything like that, let alone score 16 runs.”

Andrew Benintendi lined a three-run double and Holt tripled home two more in a seven-run fourth inning that quickly turned the latest playoff matchup between these longtime rivals into a laugher. Handed a big early lead, Nathan Eovaldi shut down his former team during New York’s most lopsided defeat in 396 postseason games.

“An embarrassing day,” shortstop Didi Gregorius said.

Game 4 is tonight in the Bronx, where the 108-win Red Sox can put away the wild-card Yankees for good and advance to the AL Championship Series against Houston. Rick Porcello is scheduled to pitch against New York lefty CC Sabathia.

Boston battered an ineffective Luis Severino and silenced a charged-up Yankee Stadium crowd that emptied out fast on a night when Red Sox rookie manager Alex Cora made all the right moves.

By the ninth, backup catcher Austin Romine was on the mound for New York and he gave up a two-run homer to Holt that completed his cycle .

“You get a little antsy when a position player is on the mound. I told everyone, ‘Get me up. I need a home run for a cycle,’” Holt said. “I scooted up in the box a little bit, and I was going to be swinging at anything and try to hook anything. Obviously, you don’t expect to hit a home run, but I was trying to. I was trying to hit a home run. That’s probably the first time I’ve ever tried to do that. I rounded the bases, and seeing everyone going nuts in the dugout was a pretty cool moment for me.”

His teammates, too.

“He wasn’t shy about it,” Benintendi said. “Everybody was rooting for him.”

Boosted by noisy fans in their homer-friendly ballpark, the Yankees entered 7-0 at home the past two postseasons — against out-of-division opponents. But the Red Sox, frequent visitors who clinched the AL East crown at Yankee Stadium just 2 1/2 weeks ago, were hardly intimidated.

“I think from pitch 1, we let them know that we were here,” Cora said.

Mookie Betts, in fact, hit a 405-foot flyout to the center-field warning track to begin the game.

Making his first playoff start this year, Holt opened the fourth with a single off Severino and capped the 26-minute outburst with a triple to right field. The 2015 All-Star also doubled home a run in the eighth and finished with five RBIs.

Holt also hit for the cycle against Atlanta on June 6, 2015.

“He’s been swinging the bat well for a while now,” Cora said. “We felt the matchup was good for him.”

Every starter had at least one hit for the Red Sox, who piled up 18 in all. The only time they scored more runs in the postseason was a 23-7 win over Cleveland in 1999.

Eovaldi pitched for the Yankees from 2015-16 before injuring his elbow, which required a second Tommy John surgery. Boston acquired him from Tampa Bay in July and the hard-throwing righty compiled a 1.93 ERA in four starts against New York this season — three with the Red Sox.

Bumped up a day in front of Porcello, he delivered a gem in his first postseason appearance. Eovaldi allowed one run and five hits in seven innings, throwing 72 of 97 pitches for strikes.

“I was just trying to use their aggressiveness against them and try and get some quick outs,” Eovaldi said. “It was a special moment for me. I don’t think it’s really quite settled in yet.”

Going with Eovaldi was one of several choices that paid off for Cora.

Looking to play left-handed hitters against Severino, the first-year skipper inserted Holt at second base and Rafael Devers at third. Christian Vazquez started at catcher over Sandy Leon.

Devers singled twice, stole a base, scored two runs and knocked in another. Vazquez’s infield single off Severino’s glove drove in the first run.

Benintendi, already a Yankees nemesis, was on base four times and scored twice. Betts also scored two runs and drove in two.

“It just kind of shows you what kind of team we have and that we could explode at any minute,” Betts said.

TBS reported Severino began warming up only 10 minutes before the game, and he certainly looked out of sorts from the start in misty weather. He left with the bases loaded and nobody out in the fourth and was charged with six runs and seven hits.

“He got his normal pitches routine,” Yankees manager Aaron Boone said. “It wasn’t an issue.”

STRANGE SIGHT — The only other position player to pitch in a postseason game was Toronto infielder Cliff Pennington against Kansas City in the 2015 AL Championship Series.

IF AT FIRST — There were four replay challenges in the first four innings — all involving calls by first base umpire Angel Hernandez. Three were overturned.

TRAINER’S ROOM — Red Sox: 1B Mitch Moreland sat out after leaving Game 2 when he hurt his right hamstring running the bases. “Mitch is available, but he’s not 100 percent,” Cora said. Steve Pearce played first and had an RBI single in the fourth.

Yankees: CF Aaron Hicks remained out of the lineup after missing Game 2 with tightness in his right hamstring, which forced him from the series opener Friday. Boone said Hicks was doing “significantly better,” and sitting him was a much more difficult decision than it was Saturday. Brett Gardner was back in center, but Boone said he wouldn’t hesitate to use Hicks in any role off the bench.

UP NEXT — Red Sox: Porcello (17-7, 4.28 ERA) got two late outs in relief during the series opener last Friday, so his start was pushed back a day to Game 4. The 2016 AL Cy Young Award winner, who grew up a Mets fan in nearby New Jersey, was 2-0 with a 2.31 ERA in three starts against the Yankees this year — including a one-hitter on just 86 pitches Aug. 3 at Fenway Park. He is 0-3 with a 5.33 ERA in 12 career postseason outings, including four starts.

Yankees: The 38-year-old Sabathia (9-7, 3.65) will be on 11 days’ rest when he makes his 23rd postseason start. The big lefty was ejected from his last regular-season outing for hitting Tampa Bay catcher Jesus Sucre with a pitch during a testy game between division rivals on Sept. 27. Sabathia appealed a five-game suspension from Major League Baseball that would not take effect until next season. He said Monday he definitely wants to play in 2019 — even if it’s not for the Yankees.