BOSTON — Before Red Sox first baseman Kyle Schwarber cemented his status as a big-game performer, he was just a high school senior trying to impress a visiting college coach.

It was 2011, and Schwarber, a star for Middletown High School in Ohio, was well aware that Tracy Smith, then the head coach at Indiana University, was there when he belted three home runs in a game. Seeing how calm the young player was under pressure, Smith didn’t take long to make him an offer.

“Great players do great things,” Smith said. “They seize those opportune moments.”

Schwarber’s knack for rising to the occasion followed him to college and then to the majors. Smith remembers Schwarber’s go-ahead home run in the Big Ten championship game in 2014, and his World Series performance in 2016, when he hit .412 after coming back quickly from major knee injuries, establishing himself as one of the curse-breaking heroes of Chicago’s North Side.

On Sunday, Schwarber was back to his old tricks, this time for the Red Sox, collecting three hits, including a leadoff home run, in Boston’s wild 6-4 win over the Tampa Bay Rays in Game 3 of their American League division series.

Schwarber, 28, has hit .305 with a .412 on-base percentage and eight homers across 28 career playoff games, most of which came with the Cubs. In 2016, he and a nucleus that included Kris Bryant, Anthony Rizzo and Javy Baez delivered the organization’s first championship since 1908. But that core never won another ring, and Chicago spent the past year disbanding the group. Bryant went to San Francisco before the trade deadline, Rizzo to the Yankees and Baez to the Mets.

Schwarber, who was nontendered in December after a down year for Chicago, was the first of the bunch to go. “He was very thankful for his time with the Cubs,” Schwarber’s father, Greg, said. “He honestly believed he’d be with the Cubs still.”

Instead, Schwarber spent the first half of the 2021 season with the Washington Nationals after signing a one-year deal in January. He thrived for Washington, hitting 16 home runs in an 18-game span from June 12 to 29. A hamstring injury and a fire sale of star players put an end to his Nationals tenure soon after.

Boston acquired the injured slugger on July 29. He finally got on the field for the Red Sox on Aug. 13 and proceeded to hit .291 with seven homers and 18 R.B.I. in 41 regular-season games. From Aug. 13 through the end of the regular season, his .957 on-base plus slugging percentage was the 13th best in the majors among players with at least 150 plate appearances, just ahead of Giancarlo Stanton of the Yankees.

Drafted fourth overall by the Cubs in 2014, Schwarber had not known any other organization before this season and has had to adjust to a life on the move — a situation exacerbated by his being eligible for free agency this off-season if he and the Red Sox do not exercise a mutual contract option.

“It is what it is,” Schwarber said. “It’s just part of the game. It’s the business side. There’s not many guys in any organization that you see stay their whole career. When you do see that, it’s very special. I’ve been lucky to be in a winning organization with the Cubs where we went to the playoffs five out of six times.”

Of his short time in Washington, he lamented that the team did not play up to its ability.

“We were really good on paper, and the injuries kept piling up on us,” he said. “And the trade happens, and you come into a really good situation where you’re pushing for a playoff race here. That’s all you want as a baseball player, just to be in that kind of atmosphere and that situation.”

Schwarber reflected on his year of change ahead of Game 3 on Sunday, which Boston won in 13 innings. In addition to his stellar hitting, Schwarber, often a social media darling, delivered a self-deprecating viral highlight by enthusiastically celebrating his execution of a routine underhand throw to first base. He had previously botched a similar play.

The win gave Boston a two-games-to-one advantage in the series, with a chance to end the Rays’ season on Monday night.

Schwarber, who also drilled a home run off Gerrit Cole, the ace of the Yankees, in the A.L. wild-card game, is 6 for 16 in what he hopes are the early stages of his first postseason with the Red Sox. His uniform has changed, but Schwarber is thriving under pressure.

“There’s certain people that just step up in moments like that. He’s always been one,” said Fred Nori, a longtime coach and a friend of Schwarber’s from Middletown. “As far as what causes all that, if anybody can figure that out, it’d be interesting. There’s just certain guys that do. He always has.”

Nori and others reasoned that Schwarber’s football background — he played linebacker in high school — helped develop his flair for the dramatic. “He’s just been cool with it,” said Nori, who referred Schwarber to Smith. Smith mentioned a “blend of humility and confidence.” Schwarber’s newest manger, Alex Cora, credited the Cubs’ system of development.

“It seems like that group from Chicago, all those kids, they understand what it takes to be a winner,” Cora said.

“One thing with him — and I think it’s more about Fenway, Boston, the passion — he played in a very similar atmosphere in Chicago,” Cora continued. “With him, this is not that different.”

Schwarber chalks his postseason success up to an abundance of opportunities.

“I’ve been lucky to be on really good teams in college and the minor leagues and early in the big leagues,” he said. “I got to experience the wild card and go in an N.L.C.S. my first year. Then going and winning a World Series the second year, another N.L.C.S. my third year. You can lean back on experience when you’re in big things like this.”

Third baseman Rafael Devers and Cora praised Schwarber’s clubhouse presence this postseason, with Cora noting his influence on the rookie first baseman Bobby Dalbec. “He feels like he’s been here for 10 years,” Cora said.

While Schwarber’s status with the Red Sox will remain up in the air into the early part of the off-season, he has plans to find some familiarity after a hectic year. He and his wife, Paige, are building a house near Middletown, and Schwarber and his father are looking to revive youth baseball, a costly endeavor, in a once-booming steel town that’s “struggling to find its identity again,” Greg Schwarber said.

“I love my hometown. It’s part of the person I am today,” added Kyle Schwarber, whose three sisters also live nearby. “It’s a really special place.

“It’ll be nice to be back home.”