LOS ANGELES -- Howie Kendrick and the Washington Nationals got down again but were never out -- and they finally ended their streak of playoff series futility in grand fashion.

Kendrick hit a tiebreaking grand slam in the 10th inning and the Nationals, boosted by a lightning rally against Clayton Kershaw, beat the Los Angeles Dodgers 7-3 Wednesday night in Game 5. They advanced to the NL Championship Series starting Friday at St. Louis.

"I was hoping for any moment," said Kendrick, a 36-year-old veteran who was hitless in his first four at-bats.

In their first season since star slugger Bryce Harper left as a free agent, the Nationals became the first team in major league history to rally from three or more runs down twice in elimination games during the same postseason.

"It's not just one player, it's a team," left fielder Juan Soto said.

The wild-card Nationals won a playoff series for the first time since the team moved to Washington ahead of the 2005 season, and the franchise reached the NLCS for the second time in 51 seasons. The Nationals overcame a 19-31 start, finished 93-69 and then rallied from a 3-1, eighth-inning deficit to beat Milwaukee 4-3 in the NL wild-card game.

Then they bounced back from down 2-1 in the series against the Dodgers, who set a team record with 106 regular-season wins.

"Oh, man, keep fighting," Anthony Rendon said. "I think that's the story of maybe this organization."

Rendon and Soto homered on consecutive pitches to overcome a 3-1 deficit in the eighth against Kershaw, a three-time Cy Young Award winner. Soto had started the comeback from a 3-0 hole with an RBI single in the sixth off starter Walker Buehler and then hit a 449-foot drive halfway up the right-field pavilion off Kershaw, the longest home run of the 20-year-old's big league career.

Adam Eaton walked against Joe Kelly leading off the 10th, Rendon doubled on a drive that lodged in the left-field wall and Soto was intentionally walked.

Kendrick was 4 for 19 with one RBI in the series and had made a pair of errors at first base in the Game 1 loss. He fouled off a pitch and then hit a 97 mph fastball over the wall in dead center for his second career slam. The other was a game-ending, 11th-inning drive against San Francisco in August 2017. Cody Bellinger chased the ball all the way to the wall, putting his arms up against the fence as he ran out of room.

"It was electric. Probably the best moment of my career," said Kendrick, a 14-year big league veteran who played for the Dodgers and Los Angeles Angels. "We never gave up. The city had faith in us. The fans had faith in us. We believed in ourselves, everybody came through for us."

Dodgers fans started exiting as the bases emptied, realizing their team's streak of NLCS appearances would not reach four.

"I'm looking in the crowd," Rendon said. "I'm enjoying it."

The seven-time defending NL West champion Dodgers remain without a World Series title since 1988.

"Disappointing is probably an understatement," manager Dave Roberts said.

Daniel Hudson got the win, retiring Will Smith on a drive to the right field warning track with one on and one out in the ninth, then getting Chris Taylor on a liner to center.

Sean Doolittle pitched a perfect 10th for Washington, with center fielder Michael A. Taylor making a diving catch on Justin Turner for the final out.

The Nationals/Montreal Expos franchise won a postseason series for only the second time, the first since the Expos beat Philadelphia in a 1981 Division Series caused by the midseason players' strike only to lose to the Dodgers in the NLCS.

"I'm really excited for the boys in that clubhouse that fought all year," Nationals manager Dave Martinez said.

Kershaw sat on the bench after the home runs, looking forlorn, bowing his head and holding it in his hands. He has a 4.43 ERA in 32 postseason appearances, nearly double his superb 2.44 ERA over a dozen regular seasons.

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

The left-hander had replaced Buehler with two on and two outs in the seventh, and struck out Eaton on three pitches. Roberts didn't second-hesitate to stay with Kershaw in the eighth.

"He's probably the best pitcher of our generation," Roberts said. "It just didn't work out. There's always going to be second-guessing. I'll take my chances any day on Clayton."

Washington's Stephen Strasburg fell behind 2-0 after eight pitches. Joc Pederson doubled on a drive that went through an opening in the left-field wall -- the crowd saw it land in the seats and thought it was a home run _ but he was awarded the double after a video review. Max Muncy, who had been 0 for 12 against Strasburg, drove a fastball over the center-field wall.

Kike Hernandez homered on Strasburg's second pitch of the second inning, another fastball, for a 3-0 lead.

Strasburg gave up three runs and six hits in six innings, struck out seven and walked one.

Buehler allowed one run and four hits in 6 2/3 innings before Kershaw came in.

There was a scary moment when Buehler hit Kurt Suzuki on the left wrist and the ball shot up and knocked off his helmet as the ballpark went silent. Suzuki fell to the ground, grabbing his face. He walked off his under his own power and was replaced by Yan Gomes, who moved behind the plate in the bottom half.

WORLD SERIES

The Series will start in the American League ballpark because all the Astros (107), Yankees (103) and Rays (96) all finished with more wins than the Nationals or Cardinals (91).

SLAMMING

Nelson Cruz hit the only previous extra-inning postseason slam, for Texas against Detroit in Game 2 of the 2011 ALCS.

UP NEXT

RHP Anibal Sanchez (11-8) is the most likely candidate to start the NLCS opener.