BOSTON -- Nathan Eovaldi was at his "Nasty Nate" best in Tuesday night's American League Wild Card showdown with the Yankees, and he looked poised to carry his team through seven innings or so.

But Red Sox manager Alex Cora pulled the plug on his battle-tested righty at his first hint of trouble in the sixth inning.

It would have been a second-guessable moment if it backfired.

However, things tend to have a way of working out in October for Cora, who once again made all the right chess moves in a big game. His Red Sox responded by pulling out a 6-2 victory that vaulted them into the AL Division Series for a matchup with the Rays that will start Thursday night at Tropicana Field.

Eovaldi fired 5 1/3 tremendous innings on only 71 pitches, allowing four hits and a run while walking none and striking out eight.

It isn't really going out on a limb to say that most managers would have kept going with the starter in that situation. But Cora got exactly what he wanted from Eovaldi, and then asked him for the baseball.

Eovaldi walked off to the thunderous ovation he deserved, and Cora asked his 'pen to get him the final 11 outs, clinging to a 3-1 lead at the time.

"Nate was great," said Cora. "When I went to the mound, he gave me this look, like, 'What are you doing?' It's a tough game to manage, of course. If it's a five-game or seven-game series, we'll keep him there. But the way our bullpen was and the way we feel about them, I felt like that was the time."

Begrudgingly, Eovaldi understood. Perhaps that's because he watched Cora make similar maneuvers three Octobers ago.

"It's definitely frustrating, but obviously I understand the situation and everything," said Eovaldi, who slimmed his career postseason ERA to 1.63 in seven appearances. "Third time through the lineup, it's tough. Batters seeing you for the third time, they have a better understanding of what you're going to do and a better idea of how you're going to attack them. I get it."

Ryan Brasier -- one of the 2018 heroes -- was first up in relief, and he got some help from his friends in the field. Giancarlo Stanton hit a rocket that just missed being a homer and it caromed high off the Monster. Kik¨¦ Hern¨¢ndez fielded the carom, then Xander Bogaerts took in the relay throw and fired a strike to the plate, where Kevin Plawecki tagged out Aaron Judge, again taking Fenway to the highest decibel levels possible.

Nobody had a bigger sigh of relief at the end of that perfectly executed play than Cora.

"We almost got burned, but Kik¨¦ made a great play and [Plawecki] a great tag, and then after that, everyone settled down and we got 27 outs," said Cora.

Of all the things Cora missed during his one-year suspension, which included a departure from the Red Sox before he was rehired, managing in October was at the top of the list.

"It's fun," said Cora. "This is why you want to be a big league manager. I just got lucky that in 2018, I had a great team and we did what we did. Obviously 2019 didn't go the way we wanted, and in 2020, we all know what happened. But to be able to play in October, we're blessed."

Cora loves the game-to-game decisions -- and not just the bullpen ones. Much of his best work comes before the bright lights come on.

Prior to the game, knowing he was without star slugger J.D. Martinez (sprained left ankle), Cora tinkered with his lineup. Kyle Schwarber moved to leadoff, flip-flopping with Hern¨¢ndez, who went to the two-hole. Schwarber had one of the biggest hits of the game, a towering solo homer to right in the bottom of the third that helped lead to an early knockout for Gerrit Cole, the $324 million ace of the Yankees.

While he was at it, Cora flipped his 3-4 combo, putting Rafael Devers third and Bogaerts fourth.

There was Devers working a key two-out walk in the bottom of the first. And there was Bogaerts, bashing a slump-busting two-run homer to center.

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"This is the first time with Kyle hitting leadoff and Kik¨¦ hitting second, and we had to do it because of the situation we're in," said Cora. "And right away, they pitch around Raffy and they pay the price. Xander put a great swing on a slider and hit it out of the ballpark, and Kyle hit the home run. I think the top of the order was amazing today. It's what they do."

And this is what Cora does. The last time Cora managed in October, he guided the Red Sox to a World Series championship with a dominant run in 2018. That team was expected to do huge things.

This year's club wasn't. Go back to the preseason prognostications in basically every publication for proof of that.

But with Cora back and getting the most out of his team, they are back in the postseason and looking dangerous.

The Red Sox are sure to be underdogs in the best-of-five series that awaits against the Rays. But with Cora at the helm, you never know what might happen.

Before shifting his attention to that, Cora reflected briefly on the grind of clinching a postseason berth on the final day of the regular season in a wild comeback at Washington on Sunday, followed by all the pressure of Tuesday.

"I thought [Game] 162 the other day was the most uncomfortable game to manage in my career," said Cora. "This tops it. This was something different."

That said, the result was quite familiar -- one Cora has become accustomed to in the most crucial month of the baseball calendar.