Jayson Werth sat next to Michael Morse in the Washington Nationals’ dugout late Sunday afternoon and explained how to properly take a curtain call. One inning earlier, Morse walked to the edge of the dugout and raised both fists into the air. Werth told him he needed to climb up the steps and bring a helmet.

The Nationals Park crowd frothed as they spoke, celebrating an electric conclusion to the Nationals’ thorough, 3-0 victory over the playoff-chasing Atlanta Braves. Sitting close together, they still had to yell over the noise. Morse laughed and apologetically informed Werth he had never taken a curtain call before.

“Get used to it,” Werth replied. “Because this place [is] going to be awesome. This is how it’s going to be the rest of the way.”

The sun-splashed final day of the Nationals’ home season and the 37,638 at Nationals Park provided a vision for how the Nationals hope next fall will unfold — taut games packed with meaning before a frenzied crowd. They have won 12 of their past 15 games, and with a sweep in Florida they would finish with the first winning record by a Washington baseball team since the 1969 Senators went 86-76.

Their performance Sunday turned the 2011 farewell into a giddy afternoon for the present and future. Ross Detwiler closed his season with six scoreless innings, further cementing his place in the 2012 rotation. Henry Rodriguez, Tyler Clippard and Drew Storen closed with an absurdly dominant final three innings, the crowd roaring with each out. Morse hit his 29th home run, a two-run, opposite-field blast in the seventh.

Around the time Morse took his curtain call, the video board at Busch Stadium in St. Louis was showing a replay of his homer to another roaring crowd. The Braves’ loss and the Cardinals’ 3-2 win over the Chicago Cubs reduced Atlanta’s lead in the National League wild-card race to one game. The Nationals had wandered into a playoff race, and in taking two of three from the Braves, they played like the team fighting for October.

“We know for a fact that we’ve got the best out of Atlanta,” Clippard said. “They’re fighting for a playoff spot, and we handled them pretty good. It gives us confidence going into these final three games and into the offseason for next year.”

Their recent opponents have let the Nationals puff their chests. They swept the 99-win Philadelphia Phillies over four games on the road, then came home, where they went 44-36 this year, and tried to ruin the Braves’ October. Afterward, they watched the Cardinals on clubhouse TVs and rooted for St. Louis.

“I definitely don’t think anything we’re doing is a fluke,” outfielder Jonny Gomes said.

Before the game, General Manager Mike Rizzo said the Nationals need only an outfield bat and one more elite starting pitcher to contend next year. If they do, they may point to Sunday as the day they convinced their fans to board the bandwagon. Detwiler compared the atmosphere to one of Stephen Strasburg’s starts.

“We have a core group of fans,” Werth said. “It’s small. There are die-hards out there. There aren’t a lot of them, not yet. It’s going to spread. It’s going to be contagious. It’s going to get good.”

Detwiler provided the most promise Sunday afternoon, allowing two walks and four hits while striking out four. He hit 95 mph with his sinker but did not seem all that pleased with his control. Perhaps he had raised his standards when he shut out the Phillies for 71 / 3 innings in his prior start.

“I think I kind of scuffled the whole game,” Detwiler said. “I think I kind of got lucky that they were hitting balls right at people.”

In 10 starts this season, Detwiler posted a 3.21 ERA over 56 innings, and in his final two outings Detwiler threw 131 / 3 scoreless innings against the NL East’s best two teams. He has succeeded by keeping his sinker low in the strike zone, but his roughest moment showed how far he has come with his mind-set.

In the third, he allowed a leadoff single to David Ross and walked two consecutive batters, including pitcher Mike Minor on four consecutive pitches. When he started leadoff hitter Michael Bourn with a 3-0 count, Detwiler had thrown eight straight balls.

Earlier in the week, Detwiler admitted that sometimes he would find trouble on the mound and think to himself, “Here we go again.” Not this time. Bourn took one strike and flied out to shallow left. Martin Prado flied to right, and Gomes’s strong throw home kept Ross at third. Chipper Jones grounded to third baseman Ryan Zimmerman, and Detwiler had escaped.

“I think he grew up a lot today,” Manager Davey Johnson said. “He got a little wild and didn’t get overly aggressive and just stayed within himself and pitched out of a tough jam.”

Detwiler left with a 1-0 lead. Morse secured the game with a home run in the seventh. As he stood at the plate, fans chanted, “Let’s go, Beast!” He delivered a blast to the opposite field over the scoreboard. The crowd would not stop screaming for Morse until he emerged from the dugout. Maybe it was flawed, but the curtain call meant a lot to Morse, the slugger no one saw coming.

“That was awesome,” Morse said. “You know, all that stuff made me who I am today. If it wasn’t for not getting to play and sit on the bench and overcoming adversity, maybe I would have never got that curtain call.”

After Storen sealed his 42nd save, the crowd gave one more ovation. They will not see baseball again until next April, and the Nationals left them wanting — and expecting — more.

“Next year,” Zimmerman said, “hopefully the fans will be here and we’ll be the ones playing meaningful games.”