WASHINGTON >> A little past midnight in Game 5 of the NL Division Series, Clayton Kershaw emerged from the bullpen to pitch in relief for the first time in seven years.

Two outs later, the only save of his major league career in the books, Kershaw’s arms were raised and teammates were rushing to celebrate with a guy whose postseason performances have never carried the luster of his regular-season success.

Coming in with two runners on base and the outcome in the balance, Kershaw got Daniel Murphy to pop out, then struck out Wilmer Difo to end it, finishing the Los Angeles Dodgers’ 4-3 victory over the Washington Nationals to win their NL Division Series in game that ended in the wee hours of Friday.

The Dodgers won the last two games of the best-of-five NLDS and now head to the NL Championship Series to face the Chicago Cubs. That opens at Wrigley Field on Saturday night.

The Nationals, meanwhile, still have never won a postseason series.

Kershaw worked two days after throwing 110 pitches over 6 2/3 innings in Game 4, when he had the benefit of only three days’ rest following his win in Game 1 against the Nationals.

Several hours before Thursday’s game began, Dodgers first-year manager Dave Roberts was asked whether Kershaw might be available at all — maybe just for one out, say?

“No,” came Roberts’ reply. “Absolutely not.”

Turned out the three-time NL Cy Young Award winner would get a pair of outs in his first relief appearance since the 2009 playoffs.

He came in after regular Dodgers closer Kenley Jansen threw a career-high 51 pitches while getting a career-high seven outs after entering in the seventh. Jansen walked Bryce Harper and Jayson Werth with one out in the ninth — and that’s when Roberts went to Kershaw.

Kershaw wound up with his second pro save. His other one came in 2006, the Gulf Coast League.

LA’s scoring all came in a four-run seventh off six Nationals pitchers, including Joc Pederson’s homer off Max Scherzer and Justin Turner’s two-run triple off Shawn Kelley.

Washington was leading 1-0 in the sixth, when Werth walked and Ryan Zimmerman smacked a two-out double to left. But third-base coach Bob Henley — whose propensity for waving runners home led to a popular T-shirt among Nationals players that says, “Send ‘em short, send ‘em tall, send ‘em one, send ‘em all” — sent Werth and saw him get thrown out easily on shortstop Corey Seager’s relay.

Wasn’t even close.

And in the sort of blink-and-you-missed-it game-shifting sequence, Werth’s inning-ending, overzealous bid to score was followed immediately by Pederson’s homer on Scherzer’s first — and, it turned out, only — pitch of the seventh. Pederson connected with a 96 mph slider, sending it to the opposite field and over Werth’s head in left.

That began a rally that included a pinch-hit RBI single by 37-year-old pinch hitter Carlos Ruiz, helping LA go up 4-1.

Then came Heisey’s homer.

Then came Jansen.

And then came Kershaw.

The West champions Dodgers are back in the NLCS for the first time since 2013, but they’ve lost in their past three trips to that round, failing to make it to the World Series since they won their most recent championship in 1988.

The East champion Nationals, under first-year manager Dusty Baker, are one-and-done in the playoffs yet again. They won their third NL East title in the past five years, but each time were eliminated in the NLDS. Washington was beaten in five games in 2012 by the St. Louis Cardinals after leading 6-0, then 7-5 entering the ninth, at home in Game 5, and in four games in 2014 by the San Francisco Giants.

Take it back further, and a baseball club based in the nation’s capital hasn’t won a postseason series since the old Senators were the 1924 World Series champions.

YOUNG URIAS

Dodgers LHP Julio Urias, who turned 20 in August, became the youngest pitcher to appear in the postseason since Cincinnati’s Don Gullett was 19 in the 1970 World Series, the Dodgers said, citing STATS. Urias entered in the fifth and threw two scoreless innings. He walked Harper, then picked him off first base.

‘RIP’ HARAMBE

According to the Cut4 Twitter feed, Harper paid tribute to Harambe, the gorilla killed at the Cincinnati Zoo, with an “RIP” decal on his bat knob during batting practice before the game.

TRAINER’S ROOM

Nationals: Baker said before the game that RHP Stephen Strasburg would not be able to pitch in the NL Championship Series if Washington were to advance. “He won’t be available for the next series,” Baker said. “It would be a miracle if he was.” That doesn’t really come as a surprise, given that Strasburg has been sidelined since hurting his pitching elbow in early September and cut short a bullpen session Tuesday.