Alex Cora went against analytics in Game 3 — and the result was spectacular

Red Sox manager Alex Cora (far right) is pictured duing pre game introductions. Jim Davis/Globe Staff

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NEW YORK — Alex Cora managed it. It’s that simple.

He saw that what he had drawn up wasn’t working. As much as he loved and believed in the lineups in the first two games, he had left two of the hotter hitters of the past couple of weeks on the bench. So even though Brock Holt and Rafael Devers had horrific numbers against Luis Severino, he put them in the lineup anyway.

This was one of those nonanalytic moments. Cora simply had a feeling, a Joe Morgan hunch, that the two lefthanded hitters would do something significant. And he was right. Man, was he right. As in 16-1 right and a 2-1 lead in the series with the possibility the Red Sox could win the clincher Tuesday.

“We know the numbers didn’t look good, but Brock’s a good player and all he needed to do was put some good swings together,” Cora said. “I knew he could do that because of the way he’s been hitting the fastball lately. He’s a good player, and he showed that tonight.”

Holt replaced Ian Kinsler at second base and hit for the cycle — the first in postseason history — with five RBI, hitting the home run in the ninth against catcher Austin Romine, who came into pitch in the blowout. Holt had two hits in his first three at-bats and had a single, triple, double, and homer in that order.

Devers singled, was credited with a stolen base, and scored on an infield single by Christian Vazquez (oh, yeah, another change) in the second inning. Devers also drove in a run when he hit into a fielder’s choice in the third.

By necessity, Mitch Moreland’s injured hamstring, Steve Pearce had to play first base. He delivered an RBI single in the fourth.

Cora also elected to flip-flop Nathan Eovaldi and Rick Porcello, so that Eovaldi would start Game 3. That worked, too. Eovaldi kept the Yankees off the board for the first three innings while the Red Sox amassed their double-digit lead and gave the Red Sox a seven-inning start.

So the magic wand, hunches, good old-fashioned gut feeling panned out nicely. Cora didn’t need anyone to spit out the formula for this one, because such a formula didn’t exist. Holt was 1-for-15 against Severino. Devers was 0-for-12. Andrew Benintendi, who tripled in three runs, had great success against Severino with an 11-for-27 (.407) mark, while J.D. Martinez also had a lofty .412 average against him.

This was an offense that was hitting .213 for the first two games. But in Game 3 in enemy territory, in one of the most hostile environments you can imagine, the Red Sox offense stopped the “Boston Sucks!” chants early on.

One of the loudest places in baseball suddenly became quiet and sullen, as the Red Sox have now taken the Yankees to the brink in this five-game series.

Holt is simply a winning ballplayer. He might not be a starting player, but he does what he does about as well as any player in baseball. He’s a sparkplug who comes up with big hits at big times. There might be a hundred players with more talent, but he works for the Red Sox, and the way he was swinging the bat late in the season, he was worthy of a start. Whether he starts against lefty CC Sabathia on Tuesday night remains to be seen. Ditto Devers, who got the nod over Eduardo Nunez. But in Game 3 it worked famously, despite all of the numbers being completely stacked against them.

“AC let me know last night that I’d be playing somewhere whether it was first or second base,” Holt said. “My numbers aren’t good against Severino, so I texted him back and said, “Are you sure?”

As much as Red Sox fans were concerned about their team after Game 2, that same concern swept over Yankeeland after this one and likely more so since the Red Sox could wrap it up.

You could see why Cora seemed so loose and not worried before the game. He was joking around with media and even went over to Yankee third base coach Phil Nevin, with whom he once had words and gestures for after an April brawl between the two teams, and they seemed to patch things up.

It’s not often a manager impacts a baseball game, because to be honest, it’s the players who impact the game the most. But if you contrast the two rookie managers Monday night, you’d conclude that Cora was an A and Aaron Boone was an F. Nobody could figure out why Boone stuck with Severino for so long while Cora’s moves were shining.

When this series was tied at 1-1, you had to start to think, would the Red Sox bow out of the divisional series for the third straight year? And if you’re the Yankees now, despite winning 100 games, if they bow out in the divisional round, that would be much worse than losing in Game 7 of the ALCS last season to Houston. The Yankees fired Joe Girardi after he led a Yankee team that really overachieved last season to that point.

Alex Cora’s lineup additions came through in Game 3, including Brock Holt, who hit for the first postseason cycle.Else/Getty Images

If the Red Sox are about to wrap this up, then Cora has earned accolades because of his 108 regular season wins and because he’s finally got the Red Sox into the ALCS. Beating the Astros, his former team, would be the ultimate satisfaction for Cora, but he needs to come up with another very good game plan to put the Yankees away on Tuesday.

Cora could have stuck with Nunez, Kinsler, and Sandy Leon, but he went against the numbers. And sometimes that’s not only the best way, but refreshing in this day and age.