On Tuesday night in Nationals Park, the entire Nats season, all 162 games of it, was recapitulated in just nine thrilling, emotionally exhausting innings as Washington rallied from a two-run deficit with three runs in the eighth inning to beat Milwaukee, 4-3, in a National League wild-card game that will assuage the hurt hereabout from three previous Game 5s in division series in this park.

To give extra power and symbolism to their inspiring win, the Nats beat the man who epitomizes the Brewers — Josh Hader, the left-handed reliever who struck out a preposterous 138 men in 75⅔ innings.

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Bring on the Dodgers in the NL Division Series that starts Thursday in Los Angeles. They’re the team that has ruled the NL with back-to-back pennants but are also the club that the Nats, behind their hands, have said that believe they can match, toe-to-toe, in a five-game series. For their past 112 games — as they went ­74-38 — the Nats tried to set the stage for that showdown. Now they’ve got it.

The Nats won with grit, with a hit batsman, with a bloop hit, with a walk and with a rocket of a two-run base hit by Juan Soto, who had been in a 5-for-47 slump that would numb the competitive soul of most 20-year-olds.

Finally, on that Soto hit, the Nats won with a bad hop — which deflected off the glove of Milwaukee right fielder Trent Grisham for an error that brought home the winning run. In other words, they won as they have all season — just as rationality and normal baseball expectations said they would not.

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An early-arriving, always-roaring, usually-standing and never-give-up crowd of 42,993 did its best imitation of a joyful madhouse as Soto’s hit and Grisham’s boot cleared the loaded bases and turned 3-1 misery into 4-3 jubilation within seconds. The Nats have practice saving their season, time after time, since they bottomed at 19-31 on May 23. Why would they forget how now?

All season, the Nats have been defined by their resilience — but also by their cussedness. All of those blown leads by their worst-in-MLB bullpen have made them stubborn in the late innings, determined to compensate for their flaw. This time, it was Hader, who strikes out as high a percentage of the hitters he faces as almost any pitcher in history, that the Nats had to defy.

Hader started that indelible eighth by fanning Victor Robles. But he didn’t strike out pinch hitter Michael A. Taylor. He hit him with a pitch — a call that was upheld after a Milwaukee challenge that the ball had struck the knob of Taylor’s bat first before it hit his hand. By the 10th replay, it looks as if the ball hits bat and hand simultaneously — a perfect tie. So, the original call stands. That’s the margin of error — basically nothing — by which a rally that saves a season starts.

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After Trea Turner struck out, it seemed the baseball world had been restored to order. One more Nats whiff and the inning would be over with only the ninth inning left to traverse — a normal two-inning save task for Hader.

But the southpaw did not strike out pinch hitter Ryan Zimmerman, clutch hitter supreme in his youth and prime but now a tough old vet begging his body to let him play a few more games. With two outs, Zimmerman shattered his bat but dumped a beautiful, humpbacked flare into center field for a single. At first base, a sheepish Zim smiled.

Keep the line moving, and the heart beating, any way you can.

And Hader, with his laser fastball and sweeping breaking ball, did not strike out Anthony Rendon, either. As the crowd chanted, “MVP! MVP!” throughout his at-bat, he worked a walk to load the bases. Are you feeling it yet? Are you remembering where you were, whether you watched it at Nationals Park or on TV live or, for the poor unfortunates, when you only saw it on replay?

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Above all, Hader did not strike out Soto, the kind of left-handed hitter he is supposed to dominate, intimidate and fit for a dunce cap.

Instead, Soto lashed a rocket to right field on a letter-high fastball, a 100-plus-mph bullet that was certain to be a two-run, game-tying blow. Taylor and swift young pinch runner Andrew Stevenson were sure to score.

That’s when the bad hop happened — the best bad hop in Washington baseball since the one in the final inning of the 1924 World Series when Earl McNeely’s bouncer hit a rock — a stone or pebble that some searched for for days — and jumped over the head of Giants third baseman Freddie Lindstrom as the winning Senators run dashed home in the 12th inning. You don’t have to remind me. A photo of that moment dominates my Facebook page.

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Grisham, 22, a rookie with 51 games in the majors who was playing because injured superstar Christian Yelich is out for the season, decided, in the fraction of a second that baseball allows, to charge Soto’s hit, hoping to grab it on the first bounce and fling it home. It was probably a futile idea. If Grisham had a voice of experience in his head, it would have screamed, “BE CAREFUL.” But hope, blind dumb hope, in the instant when your team’s 3-1 lead is turning into a 3-3 mess, seldom holds away.

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Grisham raced in at the edge of recklessness. And Soto’s drive, with side spin or perhaps an imperfection in the outfield, skidded to Grisham’s right, off the edge of his glove and — trickle, trickle, like blood dripping — traveled toward the right field warning track.

By the time Grisham could fetch the nefarious sphere and fling it back to the infield, Rendon had sped home all the way from first base with the fourth — and winning — run.

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The Washington bullpen which, as the world knows, has never done anything right in its collective existence, turned to Daniel Hudson, the trade-deadline addition of GM Mike Rizzo. All he did was nail down the save, allowing only a single and getting the last out on a solid fly to jubilant, retreating center fielder Victor Robles.

This three-run rally, which will loom larger the longer the Nats stay alive in these playoffs, was also a reprieve for the Nats decision-makers for what would have been a long cold winter of second-guessing — by others, but, probably, in their darker and most honest moments, of themselves.

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For 10 days, at least, Washington fans have debated: Max or Stras? Who should start this wild-card game, Max Scherzer, the three-time Cy Young Award legend but injured much of the second half of the season and dragging a 6.11 ERA in his past three starts? Or Stephen Strasburg, 18-6 this year and roaring to the wire with a 1.76 ERA in his past nine starts?

The Nats picked wrong. But they survived it.

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Scherzer walked the first batter of the game, then grooved a first-pitch fastball to the second Brewer — Yasmani Grandal, who bashed it into the Nats’ bullpen in right field for a 2-0 lead.

Then, to start the second inning, a soft Scherzer curveball looked tasty to Eric Thames, who smashed it over the right field scoreboard for another home run and a 3-0 lead. A Turner solo homer in the third off Brewers starter Brandon Woodruff was the Nats’ only early rebuttal.

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As if to turn this game into a kind of baseball laboratory experiment — one that would not satisfy the scientific method but will certainly animate a thousand water cooler debates for months — Strasburg relieved Scherzer after five shaky innings. Where Max was in constant trouble, stranding men in scoring position in three innings, Strasburg breezed through three dominant innings, allowing two hits, no walks and fanning four while making Brewers hitters look silly at times.

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Now, it doesn’t matter. Now the Nats move on to Los Angeles with $140 million free agent lefty Patrick Corbin on normal rest to face the Dodgers. Like several wild-card winners before them, the Nats arrive with the mystique of a pressure win in a the-season-is-almost-lost comeback.

No, this franchise and this fan base has never had such a win before — to set off an infield celebration and a clubhouse champagne bath for all. Are such wins contagious?

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Victories like this, rallies like this against, perhaps, the toughest reliever the Nats will face in the whole postseason, are the stuff that build a sense of mojo rising, of dreams coming into focus, for a hot team.

For weeks, the Nationals have said that they are clicking so well, and enjoying one another’s grinning rowdy company so much that they just want to keep on playing. What a magnificent way they chose to prove just how much. And for who knows how long?