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One team is playing in its 10th N.L.C.S. in the last 20 seasons. The other is playing in its first ever.

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CreditCreditJulio Cortez/Associated Press

ST. LOUIS — His team’s hometown is a hotbed of espionage, but even by Washington standards, this is a bold surveillance operation. While the Nationals face the St. Louis Cardinals in the National League Championship Series, one of their top scouts will be staying at the home of the manager of a potential World Series opponent.

The scout is Bob Boone, and the manager is his son, Aaron, who guided the Yankees to the American League Championship Series. Bob Boone, a vice president and senior adviser for the Nationals, will track the Yankees’ games against the Houston Astros in the A.L.C.S. He will do it by commuting to the games in New York from Aaron’s home in Connecticut.

“I’ll ride in with him; I won’t even need a car,” Bob Boone said in Los Angeles late Wednesday night, after the Nationals had roared back to win Game 5 of their division series at Dodger Stadium. “But he never talks too much about baseball, anyway. And he’s on the stat-side, big-time — and that just starts an argument with me.”

Boone laughed. The Nationals’ party in the visitors’ clubhouse had subsided; bubbly was seeping into the carpet, and corks and empty bottles were strewn around his feet. Boone is 71, decades removed from his last time toasting a playoff series victory. The most memorable one had a particular relevance to his current team.

Boone was the catcher for the Philadelphia Phillies, who won the best-of-five N.L.C.S. in 1980 after losing that series in 1976, 1977 and 1978. The victory, a five-game thriller with the Astros, unburdened a roster that had come to be defined by October futility. The Phillies went on to beat Kansas City for their first World Series title.

The Nationals also seek their first championship, and the opportunity was hard-earned. They lost the best-of-five division series four times before their triumph over the Dodgers.

“It’s kind of the same thing, blowing a bunch of them,” Boone said. “We had lost three playoffs, and that Houston series was ridiculous. When we got past that, we knew we were going to beat them. We just relaxed, and we knew we’d beat these guys. We were a clutch team, just like these guys.”

The Nationals? Clutch? Until this month, they had the opposite reputation. But then came their comebacks in the wild-card game against Milwaukee and the N.L.D.S. clincher in Los Angeles. Both times, the Nationals trailed by two runs in the eighth inning while facing an All-Star left-hander. Both times, they rallied to win.

“Keep fighting,” said Anthony Rendon, the Nationals’ star third baseman. “I think that’s the story of, maybe, this organization. We have always either done really, really well and then came up short, or we had been plagued with injuries and had to continue to fight out of a hole that we dug ourselves in the beginning of the year. So we just wanted to keep believing in ourselves and not worry about what people outside of our locker room were saying.”

Rendon scored the go-ahead run off the Brewers’ Josh Hader in the wild card game, after right fielder Trent Grisham misplayed Juan Soto’s two-run single. On Wednesday, Rendon homered off Clayton Kershaw to pull the Nationals within a run, and Soto homered on the next pitch to tie it.

With one on in the 10th inning, Rendon doubled off Joe Kelly, who walked Soto intentionally before serving up the most seismic hit in Nationals’ history: a go-ahead grand slam by Howie Kendrick.

It was fitting that Rendon and Soto helped saved the Nationals from the brink. They were the only set of qualified teammates in the majors who both had a .400 on-base percentage and a .500 slugging percentage in the regular season. They combined to hit .343 in the division series, and the rest of the Nationals hit .198.

“They’re tough — and they’re tough because they’re plate-disciplined more than anything,” said Matt Wieters, the Cardinals’ backup catcher and a former National, referring to Rendon and Soto. “They’re not going to help you out.”

The Cardinals’ two sluggers, Paul Goldschmidt and Marcell Ozuna, were also at their best in their five-game division series with the Atlanta Braves, both hitting .429 with two homers. Catcher Yadier Molina, the Cardinals’ emotional leader and pitching whisperer, forced the finale with tour de force in Game 4, tying it with a single in the eighth and winning it with a sacrifice fly in the ninth.

The Cardinals are playing in their 10th N.L.C.S. in the last 20 seasons, and Molina has been there for the last eight. He is seeking his fifth trip to the World Series.

“You know you have someone back there who has probably seen just about any situation you can imagine in a baseball game unfold,” said the Cardinals starter Miles Mikolas, who was scheduled to face Anibal Sanchez in Game 1. “He’s been there, he’s seen it and he’s seen it from the catcher’s viewpoint, which is probably the best one to have. The whole team feeds off that.”

The Nationals did not attempt a stolen base against the Dodgers, but they tied with the Cardinals for the N.L. lead in steals in the regular season, so Molina’s arm could be an important weapon. He will work with starters Adam Wainwright in Game 2, Jack Flaherty in Game 3 and Dakota Hudson in Game 4.

The Nationals have not announced their rotation beyond Sanchez, but they will surely lean heavily on Max Scherzer, Stephen Strasburg and Patrick Corbin, who have worked 36 of the team’s 54 innings this postseason. All three have also appeared in relief.

“They have three of the best starting pitchers in baseball,” said Walker Buehler, who started for the Dodgers on Wednesday. “Any time you can throw those three guys out there, you’ve got a chance.”

The Nationals have had many other chances to get to this round. They squandered all of them, but now they have broken through. With four more victories, they might be able to put a certain scout’s reconnaissance to use.

Tyler Kepner has been national baseball writer since 2010. He joined The Times in 2000 and covered the Mets for two seasons, then covered the Yankees from 2002 to 2009. @TylerKepner