By the time Soto signed with Washington — from the Dominican Republic for $1.5 million in July 2015 — the Nationals had lost another division series, to San Francisco in 2014. They fell again in that round in 2016 (to the Dodgers) and 2017 (to the Chicago Cubs).

“I know they always go to the playoffs, they always lose, something like that,” Soto said. “But now we’re here, we try to fight, and we’re going to see how far we’re going to get.”

Soto, now in his second season, helped the Nationals storm back from a 19-31 start by hitting 34 homers with 110 runs batted in, a .401 on-base percentage and a .548 slugging percentage. Only two other players have reached all those numbers at age 20 — Mel Ott for the Giants in 1929 and Alex Rodriguez for Seattle in 1996 — and they did not end those years in the postseason.

“He’s 20 years old, man,” said Nationals catcher Kurt Suzuki, who turns 36 this week. “I was in college at 20 years old. This guy’s hitting 30 and 100 in the big leagues at 20 years old, playing in the postseason. He’s a joke.”

The Nationals have thrived by developing high-impact stars like Soto, Stephen Strasburg, Anthony Rendon and Ryan Zimmerman, and all played pivotal roles in the eighth.

Strasburg kept the deficit at 3-1 with his third shutout inning, capping his first relief appearance since 2007, when he was a freshman at San Diego State. With two outs and one on, Zimmerman — the first player the Nationals drafted after moving from Montreal in 2005 — punched a broken-bat pinch-hit single to center. Rendon, who only led the majors in R.B.I. this season, then walked to load the bases.

Soto cleared them with help from Grisham, who said he charged too quickly on the hit, which “took a funny hop” on him and rolled away, taking Milwaukee’s season with it.