WASHINGTON — Washington’s Juan Soto delivered a bases-loaded single against Josh Hader that scored three runs with two outs in the bottom of the eighth inning, and the Nationals rallied to beat the Milwaukee Brewers 4-3 in the NL wild-card game Tuesday night.

After Hader loaded the bases by hitting one batter, walking another and allowing a bloop single, Soto took a 96 mph fastball to right, and the ball skipped under outfielder Trent Grisham’s glove. That error allowed one of the runs to cross the plate and Soto to get to second, then turn for third.

Eventually, Soto, a 20-year-old outfielder, was caught in a rundown to end the inning, but that didn’t matter: He had turned a 3-1 deficit into a lead, and so he clapped his hands, then pounded his chest and high-fived third base coach Bob Henley, shouting “Let’s go!”

Stephen Strasburg threw three scoreless innings to earn the win in the first relief appearance of his major league career, regular season or playoffs. Daniel Hudson pitched the ninth for the save.

Hader, the Brewers’ standout closer, started the eighth inning on the mound as Milwaukee manager Craig Counsell was trying to get a two-inning save out of him.

Hader took the loss.

The Nationals, so familiar with playoff heartache, advanced to face the NL West champion Dodgers in the best-of-five Division Series. Game 1 is Thursday in Los Angeles.

Washington had been 0-3 in winner-take-all postseason games, all NLDS Game 5 losses at home.

Matt Adams, a first baseman for the Nationals, played college baseball at Slippery Rock University.