The final out burrowed into catcher Kurt Suzuki’s mitt and closed a chapter in Washington’s baseball history. The strike-three slider Drew Storen threw past Hanley Ramirez on Thursday night ended the woebegone era, when this city was forced to either watch a hapless team or dream of having one.

The scoreboard at Nationals Park flashed “NATS CLINCH” in huge, white block letters. The 30,359 fans exulted. Red and white fireworks exploded into the starless sky, and smoke hovered over the field as the players pulled on red shirts and gray hats emblazoned with words once foreign to the nation’s capital: “Playoffs” and “postseason.”

The Nationals’ 4-1 victory over the Los Angeles Dodgers clinched Washington’s first baseball postseason in 79 years, an achievement that sent fans into delirious celebration and caused a knock on Manager Davey Johnson’s office door not long after 10:02 p.m., when the last pitch crossed the plate.

He was in his office, saying good night to his wife, Susan. Players dragged him into the clubhouse, where a long table had been set up. Bottles of Korbel and empty flutes had been placed on top. Every player got a glass. “Of course,” right-handed pitcher Jordan Zimmermann said in reference to Bryce Harper, the team’s underage outfielder, “Bryce had water.”

His team encouraged Johnson to speak, and the 69-year-old manager, back in the playoffs for the first time in 15 years, responded not with a valedictory, but a rallying cry.

“We ain’t done yet,” Johnson said.

The Nationals toasted and sipped the champagne. They did not spray it. The victory had guaranteed only a wild-card berth, a one-game play-in. As they acknowledged the moment, they kept their sights set higher.

“This is no doubt a big day for this organization and this city,” first baseman Adam LaRoche said. “Not to downplay the day at all, but guys aren’t satisfied at all. We don’t look at this like mission accomplished.”

The victory lowered the Nationals’ magic number to clinch the National League East to eight with 13 games remaining, and it increased their lead to 51 / 2 games over the idle Atlanta Braves. They also stayed a half-game ahead of the Cincinnati Reds, who won Thursday afternoon, for the best overall record in the majors.

“That was fun,” Johnson said of clinching at least a one-game playoff. “But that’s not what I had my eye on.”

That they had clinched any kind of playoff berth, though, begged for reflection. Owner Ted Lerner, the Rockville native who made a fortune in real estate and bought the team in 2006, stood outside the clubhouse, holding one of the hats in his left hand. “Great,” he said, unable to find any more words. “Great.”

Ryan Zimmerman gave an interview on the field, as he was the first player to yank one of the shirts over his head. He was the Nationals’ first draft choice in 2005, not long after the franchise stopped operating out of trailers in the RFK Stadium parking lot. He played on teams that lost 298 games from 2008 to 2010. He moved here for the offseasons, signed a career-long contract and proposed to the love of his life here. He stayed for the worst. Thursday night, after he ripped a double and scored a run, he experienced the best.

“It’s one of those feelings that you’ve never had before,” Zimmerman said. “We accomplished something that none of us here on this team have ever done. I think other guys have done it on other teams with other organizations. But for us to do it here and to come as far as we have, it’s a sense of satisfaction, I guess is the best word.”

Next to Zimmerman, Jayson Werth sat on a stool in front of his locker. He had come here in December 2010 from the Phillies, the reigning National League pennant winners. He became the Nationals’ first huge free agent signing with a $126 million contract and he vowed to help bring Washington a winner. Few believed him.

Werth heard talk in recent days of the Nationals not celebrating the wild-card berth at all, and he put a stop to it. “Anytime you get to the postseason, it’s a huge accomplishment,” Werth said. “We should relish this moment. The organization, and the town of Washington, D.C., should be proud.”

The Nationals clinched behind left-hander Ross Detwiler, who allowed three hits, walked one and struck out five in six innings. For the season, he has a lower ERA (3.10) than Stephen Strasburg (3.16) in only 21 / 3 fewer innings.

“Masterful,” Johnson said. “He’s just growing up as a pitcher.”

Zimmerman started the offense with his RBI double off Dodgers left-hander Chris Capuano in the third, then by dashing home on a wild pitch. Danny Espinosa lashed an RBI double in the fourth, and catcher Kurt Suzuki scored him with a clinical, two-strike sacrifice fly.

With a 4-1 lead, the Nationals only needed to hold on. In the fifth and sixth innings, Werth spotted signs in the stands that alerted him it would not be a normal win.

For the final three outs, Johnson chose Drew Storen, the closer who saved 43 games last year but took a setup role this season as he returned from elbow surgery. He pitched one of the best innings of his career. The crowd stood, and stayed standing, after Storen struck out Matt Kemp for the first out of the ninth. Storen bounded around the mound “like a high-test rubber ball,” Johnson said.

He finished the inning with the slider to Ramirez. He slapped Suzuki high-five, then lined up and shook hands.

“Afterwards, when I saw it on the scoreboard, I thought, ‘That’s pretty cool,’ ” Storen said. “I was wanting to get back and be a part of this team.”

The players acknowledged the crowd as they poured back into their dugout after postgame handshakes, clapping with hands over their heads.

“This is definitely a meaningful moment,” Werth said. “We’ll take it in, celebrate it tonight. Back to business, back to work tomorrow.”

The Nationals had wondered how, exactly, to celebrate. They wanted to acknowledge an unprecedented moment for the franchise. But they also wanted to remember they have more work to come, with much greater moments to come.

“Everybody is kind of asking each other, ‘What do we do?’ ” Detwiler said. “I think we’re gonna definitely blow it out on the next one.”