LOS ANGELES — Clayton Kershaw might very well go into the Hall of Fame one day on the strength of his amazing regular-season success — dragging behind him a painful October history he would rather forget.

Another chapter to his playoff woes was added Wednesday night when the three-time Cy Young Award winner squandered a two-run lead with the Los Angeles Dodgers six outs from advancing to a fourth consecutive NL Championship Series.

Pitching in relief of effective starter Walker Buehler and looking to help seal Game 5 of the Division Series against Washington at home, Kershaw gave up homers on consecutive pitches to Anthony Rendon and Juan Soto that tied it 3-all in the eighth inning.

The wild-card Nationals won 7-3 after a grand slam in the 10th by former Dodger Howie Kendrick off Joe Kelly.

“Just a terrible feeling,” Kershaw said.

Kershaw has been the heart and soul of the Dodgers almost since the time he arrived in Los Angeles as a 20-year-old touted prospect in 2008. While his body of work in the regular season is practically unmatched, he had a 4.33 ERA in the postseason — and that was before giving up two more runs Wednesday.

The left-hander entered in the seventh and struck out Adam Eaton on three pitches with two on to end the inning.

Kershaw, however, never got another out.

“I might not get over it,” he said. “I don’t know.”

Kershaw also took the loss as a starter in Game 2 of this series at home, when he gave up three runs and six hits in six innings. He has nine career postseason wins, but has lost 11 times in 32 career outings.

“Everything people say is true right now about the postseason,” Kershaw said.

If Rendon’s home run to pull the Nationals within a run was a jolt to the system, the long ball from Soto, deep into the seats in right-center, was the gut punch. Kershaw crouched on the mound before Soto’s drive even cleared the wall, removing his cap and turning his head to watch the ball land in the crowd.

Lifted by manager Dave Roberts for right-hander Kenta Maeda, Kershaw walked to the dugout with his head down, void of expression. He sat on the bench alone, slumped and sagging for a while, looking at the ground.

“He’s a pro. He’s probably the best pitcher of our generation, and for him to make himself available tonight, and got us out of a big spot right there,” Roberts said. “It just didn’t work out. There’s always going to be second-guessing when things don’t work out. I’ll take my chances on Clayton. … It’s a guy that I believe in, I trust, and it didn’t work out.”

Kelly’s struggles that followed were merely a continuation of a disappointing regular season, when the right-hander posted a 4.56 ERA in 51¹/₃ innings. What was especially cruel for the Dodgers about watching Kelly struggle was that he was a key component out of a Boston Red Sox bullpen that held down Los Angeles in last year’s World Series.

Kelly finished the season working his way through a mysterious lower-body injury that was essentially described as soreness.

The Dodgers dominated all season while winning a franchise-best 106 games and their seventh straight NL West title, but Washington was able to strike where they were most vulnerable. Los Angeles’ bullpen was a roller coaster due to inconsistent seasons from Kelly and closer Kenley Jansen, even if it did finish with an NL-best 3.78 ERA.