WASHINGTON -- The Dodgers won a National League Division Series that truly could have gone either way.

Over the course of five epic games, both teams seized control and lost it, stole runs and gave some back, got clutch hits and let opportunities pass by. In the end, the Dodgers won, 4-3, in the decisive Game 5 on Thursday, in a contest that featured 41 players, including one starting pitcher who entered as a pinch-runner and another who closed the game on one day of rest.

It was, as Dodgers first baseman Adrián González put it afterward, "an incredible series."

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After they advanced to face the Cubs in the NL Championship Series, which starts Saturday (8 p.m. ET/5 p.m. PT, FS1), many Dodgers players praised the Nationals for battling throughout the five-game set.

"They play the game the right way," Los Angeles outfielder Joc Pederson said. "You saw the games; all of them were neck and neck."

Throughout the series, the Nationals and Dodgers traded leads in tense, evenly matched games, with the final outcome perpetually in doubt. In Game 1, the Dodgers jumped ahead 4-0, then the Nationals came back to cut the deficit to 4-3 and the team's bullpens traded zeros the rest of the way. In Game 2, Washington came back from down 2-0 to win 5-2 and knot the series. In Game 3, the Nationals led by only one run until a ninth-inning rally made the final 8-3. In Game 4, the Nats erased a three-run deficit, only to give back the lead in the eighth and fall, 6-5.

And in Game 5, both teams held leads, both managers exhausted their rosters and Kershaw became the ninth-inning hero hours after skipper Dave Roberts vowed the lefty wouldn't pitch.

Afterward, Kershaw was effusive about the Nationals' effort in the series.

"These are the most difficult games to win. Just every at-bat, every pitch, it seemed like it was important," Kershaw said. "The at-bats that the Nationals had the entire series, you know, it just felt like it was a constant 2-2, foul off three pitches, seven-pitch at-bats.

"You know, [Bryce] Harper, he might not have gotten a ton of hits, but the at-bats that he had the whole time; [Jayson] Werth, the at-bats that he had the whole time; obviously [Daniel] Murphy, best hitter on the planet, and just up and down the lineup -- it just was a grind to get through."

In the end, the Nationals outscored the Dodgers 24-19 over the five games, but it's Los Angeles that moves on.

The Nationals now go home for the offseason, but they needn't hang their heads.

"They fought, they played hard, they did everything they needed to do," Gonzalez added. "My hat's tipped to them."