LOS ANGELES — The Washington Nationals and Los Angeles Dodgers played one of the classic winner-take-all NL Division Series games of this era in Dodger Stadium on Wednesday. It was a shame either team had to lose.

Come on, you don’t really think anybody from D.C., the town that hasn’t won a postseason baseball series since 1924, believes that do you?

This game wasn’t worth a 95-year wait. But it’ll do for now. Oh, it’ll do, because this shocking 7-3 Nats comeback win in 10 innings, capped by Howie Kendrick’s grand slam home run off reliever Joe Kelly, may set the stage for even more amazements to come.

“I was yelling, ‘Go, go, go!’ ” said Anthony Rendon, who was on second base watching Kendrick’s blast sail over the center field wall. “I was just ecstatic that it went out.”

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Now, after the kind of come-from-behind win on enemy grounds in a hallowed ballpark that makes teams think they have a destiny, the Nats advance to meet the St. Louis Cardinals, a surprise winner over the Atlanta Braves, with Game 1 in St. Louis on Friday.

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Don’t spill your breakfast coffee into your scrambled eggs, the way you may already have fumbled your adult beverage onto the rug at 12:41 a.m. on Thursday morning, but the Nats may now be a slight favorite to win the NLCS which puts you in — shhhh — the World Series.

The Nats rode the clutch playoff hitting of their heart of their order — Rendon, Juan Soto and finally Kendrick — to a Game 5 victory over a shattered team of superstar Dodgers. Their losses in the last two World Series are nothing compared to the devastation of losing to the underdog Nats with a 106-win juggernaut of a team.

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Once again, October-cursed Clayton Kershaw was the Dodger goat, allowing back-to-back homers to Rendon and Soto in the eighth inning to tie what had seemed like an almost certain Dodger win at 3-3. Tied with the Claw in shame was Dodger Manager Dave Roberts, who should never have let Kershaw face Rendon, who should never have left Kelly in for a second inning of relief to start the 10th and who, with at least six deeply dubious decisions, should never have gotten out of bed.

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In that decisive 10th, Kendrick stepped to the plate with the bases loaded — and his own head loaded with memories of his three errors in this series and his 0-for-4 night, including a double play grounder, on what had been a miserable evening.

Then, with the swing that began the dugout dance party of all dance parties, Kendrick blasted his a grand slam over the center field fence off a 97 mph Kelly fastball, breaking a 3-3 tie and sending the Nats to the greatest win in their 15-year history in Washington.

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“Howie’s like 45 years old and he’s still doing this,” said Rendon of the heroics by the 36-year-old Kendrick. What about all his errors, including another ball between his legs in Game 5, and several clutch failures at the plate?

“We all make mistakes,” said Rendon. “But THAT man can HIT!”

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Just eight days ago, the Nats snapped their postseason mini-jinx of losing three straight postseason winner-take-all games — all of them Game 5s in the NLDS — when they came back from a 3-1 deficit to beat the Milwaukee Brewers, 4-3, in the wild-card game. Now, after three champagne and beer celebrations within two weeks, the Nats only need two . . . no, don’t say it.

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But if the Tampa Bay Rays knock off the lordly Houston Astros in their Game 5 on Thursday, then it’s possible that Las Vegas oddsmakers will install the New York Yankees and, maybe, the Nats as the favorites to meet in the World Series. Can the 1958 movie “Damn Yankees” actually come to life? Let’s not get ahead of ourselves. But lets also not ignore the obvious — there will only be four teams left in one more day, and two of them will be the Nats and the Yankees.

Just as Kendrick will always be the hero, Dodgers regular season immortal and postseason goat Kershaw and his manager will take an endless drubbing for their contribution to this fabulous Nats stay-in-the-fight comeback win. After Kershaw, used in relief, escaped a seventh-inning jam with a 3-1 L.A. lead by fanning Adam Eaton, Roberts fell prey to the sentimentality card, sending Kershaw, the loser of Game 2, back to the mound in the eighth to face the heart of the Nats’ order.

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That lasted three pitches. Rendon blasted the second offering into the left field stands for a solo homer. Soto disintegrated the next offering — also a fastball — more than halfway up the deep right-center field bleachers for a game-tying homer.

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Just as Soto had delivered the crucial two-RBI eighth-inning hit in the Nats’ wild-card win over Milwaukee, the 20-year-old instant legend had done it again.

The Rendon-Soto combo, in late-season slumps and only rounding into form as this NLDS progressed, were at the center of every Nats run.

When the Nats looked demoralized and all but dead against starter Walker Buehler, who’d shut them out for six innings in Game 1 and had a 3-0 lead after five innings in this game, Rendon and Soto smashed him back-to-back with a double and RBI single to start the sixth. The spell was broken.

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That’s when the Nats’ wave started building slowly. Perhaps tsunamis, far off shore, send warning tides far ahead of them, splashing, then smashing against the shore.

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This is Southern California, proud of being laid back and, except for those 31 years since the last Dodger World Series victory in ’88, generally hard to annoy. What was one run? After all, their ace Buehler had, until that moment, held the Nats to a paltry three singles and no runs in 11 innings over two starts, including his Game 1 win.

Why worry. “What could go wrong?” say those who are naive to the menace lurking just below the surface of baseball.

A further diabolical sense of false security arrived in the seventh when Buehler finally exited after 117 pitches, by far the most of his MLB career, leaving two Nats on base with two outs. Headed-for-Cooperstown Kershaw, a southpaw giant, arrived in relief and immediately fanned Eaton on three pitches.

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The Nats are toast, right?

Not if you know Kershaw’s October history and the horrid black cloud that follows him in the postseason. In ’13, he went 0-2 with a 6.30 ERA in the NLDS — goat. In ’14, he was 0-2 with a 7.82 ERA in the NLDS — goat. In ’16, he lost Game 6 of the NLCS, 5-0, to the Cubs — elimination-game loser. In last year’s World Series, he started and lost Game 5, 5-1 — elimination-game loser.

This is now the FIFTH Dodgers postseason that has ended with Kershaw’s fingerprints on the weapon found next to the body.

And his manager not only let it happen, he deliberately tempted fate by pointing out that staying with Kershaw “was not analytics” but going with “the man.” As soon as Roberts hooked Kershaw, and went back to analytics and his normal bullpen usage, the next five Nats struck out. It says here: No Kershaw, no Nats in NLCS. Thanks, big guy.

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You could see the wave coming, feel the sense of danger approaching for the Dodgers, as the eighth began. Rendon and Soto didn’t wait. Except in the sense that they waited for the first two fastballs they saw. In reality, they are not so fast anymore — akin to 89 mph cutters, not the old over-95 mph Kershaw smoke.

Kershaw’s status here is so quasi-mythological that the Dodgers dare not demote him in the scheme of things. Their fans won’t stand for it. And, many here wonder, would Kershaw take any demotion from celestial status in stride?

On ’18-’19 merit alone, he probably should have started Game 3, not Game 2, ahead of superb Hyun-jin Ryu. If those lefties had been reversed, there’d have been no Kershaw out of the bullpen in Game 5. After all his jabbering since his Game 2 loss about how much he wanted to pitch in relief, he’s practically cornered his own manager into using him — and using him longer than he should.

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Sentimentality, and rule by superstar pecking order, will get you killed in baseball.

Rendon, a lowball hitter, took a curveball low. Then he took a not-so-fastball — 89 mph — into the left field stands for a gasp-evoking home run to cut the Dodgers lead to 3-2. A silence — the “oh, no, this can’t happen to noble Clayton again” hush — fell over Dodger Stadium.

Soto is a high fastball hitter. Kershaw threw him a first-pitch high fastball. Nice pitch selections. Who’s calling ’em, these back-to-back meatballs? Dave Martinez from the Nats dugout?

The crowd was spooked silent, which made it easier, so much easier to hear the crash, followed by a muted gasp, of Soto’s titanic blast.

This was legendary stuff. Make that “more legendary stuff.” Soto’s two-run single in the eighth inning of the wild-card game turned into a three-run game-winning play for the Nats, due to an outfield error. Soto’s two-run homer also gave the Nats a brief lead in Game 3 of the NLDS. Now, he’d done it again.

“We were 19-31 at one point and turned it around,” said Martinez, who clearly got the better of Roberts in this series, including getting four outs from starter Patrick Corbin in relief so that he would still have Daniel Hudson (winner) and Sean Doolittle available for the ninth and 10th innings. “They won’t quit. I couldn’t be prouder. I want to thank the fans who showed up for all those miserable days (in early season).’

“Keep fighting — that’s been the story of this whole organization,” said Rendon. “We believed in yourselves when (others thought) we weren’t going to make it — or maybe we should trade everybody away.”

That seems years away, rather than just months. When the final grand slam OMG arrived, this stadium was limp with disbelief. Just as the Nats’ dugout was aflame with jubilation.

When the NLCS comes to Washington for the first time ever for Game 3 on Monday, when the Nats get a chance to play for a spot in the World Series for the first time since 1933, there may be another location that afire with delight. It’s on South Capitol Street.

Washington, this is what a real October baseball run feels like — nothing else in sports is quite like it. It’s been a long time coming. Try to control yourself — a little — because this is only going to get crazier.