“It’s been a long time,” a jubilant Kershaw, who became a Dodger in 2008, said afterward. “It’s not erased yet. We have to win four more games, but ever since I came to the organization it’s been ‘1988, 1988.’ It’s the year I was born, so I know all this stuff. We want to make it ‘2017.’ ”

Entering this season, the Dodgers had made 10 playoff appearances since their last World Series run in 1988, when they beat Oakland in five games, but not once could they reach the final round. No other team in baseball has played in the postseason that many consecutive times without at least one trip to the Series.

In that frustrating span, the Dodgers reached the N.L.C.S. four times — 2008, 2009, 2013 and 2016 — but stumbled each year. They have also won five straight N.L. West division titles, including this year, but were bounced from the postseason earlier than they hoped each time — until now.

At the start of this decade the Dodgers went through franchise turbulence, and eventually Frank McCourt was replaced as owner of the team by Guggenheim Baseball Management, a group led by the billionaire Mark Walter.

The Dodgers began to spend, a lot. Since the start of the 2014 season, it has been they, not the Yankees, who have had the highest payroll in baseball. But the Dodgers also hired Andrew Friedman, then the general manager of the small-market and small-budget Tampa Bay Rays, to head the baseball operations.

“This ownership came in and did what they said, gave us the tools and gave us the personnel and gave us anything and everything we needed to win, and it was up to us players to achieve that,” said outfielder Andre Ethier, the longest tenured Dodger, who has been in the organization since 2006.

And while they spent $192 million over the off-season to keep three of their best players — third baseman Justin Turner, starter Rich Hill, and closer Kenley Jansen — they also filled the roster with both cheaper relievers, such as Josh Fields and Brandon Morrow, and talented young players like shortstop Corey Seager, who was the N.L. Rookie of the Year last year but did not play in this series because of a back injury, and first baseman Cody Bellinger, who may win the award this year.