Bruce Bochy stood back and watched as the players who just sent the National League’s best team home for the winter doused one another with Champagne yet again. “My little boogers,” he calls them.

“These guys, I can’t say enough about them,” Bochy said. “If somebody’s will is stronger than ours, or has a desire deeper than these guys ...”

Then his voice trailed off, letting the celebration tell the story.

The home clubhouse at AT&T Park was drenched again Tuesday after the Giants beat the Nationals 3-2 to capture their best-of-five Division Series three games to one, a testament to the old adage that great pitching always prevails in the playoffs.

The Giants were the 10th seed in this tournament, the little guys who backed their way in. Have some fun, get your participation medal, move out of the way and give the big boys room to fight.

But they refused to get out of the way, and now they are going to baseball’s final four again.

The Giants won their seventh consecutive postseason series (plus the wild-card game) and advanced to their third NL Championship Series in five years. They will play the Cardinals in a rematch of their last NLCS, in 2012.

Game 1 is Saturday, which means Madison Bumgarner will be able to start the series on normal rest.

They got there by winning three one-run games against a Nationals team that allowed the fewest runs in the majors and had a pretty good lineup to boot.

In avoiding a trip to Washington and a fifth game that nobody relished, the Giants won the decisive game with three runs that scored on a bases-loaded walk, a groundout and — the run that broke a 2-2 tie in the seventh inning — a wild pitch by rookie right-handed reliever Aaron Barrett.

“We just kind of fought and clawed and scratched,” Hunter Pence said. “We didn’t have any big extra-base hits, as I recall. If you bring that up, you have to bring up the defense and pitching. That’s why we are standing where we are right now.”

The Giants could not stop Bryce Harper, who doubled home the Nats’ first run against Ryan Vogelsong in the fifth inning and tied the game 2-2 with another homer off Hunter Strickland in the seventh.

But the biggest Washington bats, Adam LaRoche, Denard Span and Jayson Werth, mostly went missing in action in a series dominated by Giants starters Madison Bumgarner, Jake Peavy, Tim Hudson (who advances to his first LCS) and Vogelsong, who shrugged off a 5.33 September ERA and looked like the man who dominated in the 2012 posteason.

With plenty of gas in the tank after not pitching for 10 days, Vogelsong came out firing 95 mph and held Washington to two hits and one run in 52/3 innings, then handed a 2-1 lead to a bullpen that was as good as ever the entire series.

“I was hoping it wouldn’t get to me,” Vogelsong said. “I was hoping we’d sweep. But I had a crazy feeling it was going to come down to me in Game 4, and I just had to get the job done.”

Remember that defense Pence mentioned? He provided the series’ signature play on Vogelsong's final pitch. Pence raced back, leaped, crashed into the fence and held onto the ball as his glove smacked a padded brick archway.

Pence made a great sliding catch two years ago in Cincinnati with Vogelsong pitching, in a must-win Game 3 of a Division Series against the Reds.

Asked why it seems Pence is always there to save him, Vogelsong smiled and said, “He has to. He doesn’t have a choice.”

The Giants took a 2-0 lead with two gift runs against Gio Gonzalez, who got to play goat on the mound a day after Madison Bumgarner did.

With one out in the second inning, Brandon Crawford singled to left. Juan Perez then hit a comebacker that Gonzalez should have speared, but he deflected it to nobody and both were safe.

Once again, a bunt proved huge. Vogelsong dropped a beauty up the third-base line that died on the grass. Gonzalez and third baseman Anthony Rendon played “I’ve got it, you take it,” and Vogelsong had a hit as nobody grabbed it.

That loaded the bases for Gregor Blanco, who took four straight balls to force home the game’s first run. Joe Panik then got the second run home with a groundball, his 13th consecutive out.

Panik broke that streak with a fifth-inning single, then singled again with one out in the seventh against lefthander Matt Thornton. Buster Posey singled, too, and Pence walked against Barrett to load the bases for Pablo Sandoval.

Barrett bounced his 2-1 pitch to the backstop, and Panik scored what proved to be the series-winning run.

Sergio Romo inherited the one-run lead and got three flyballs before Santiago Casilla saved it in the ninth, getting Wilson Ramos on a grounder to set off the party.

An offensive juggernaut? Not exactly. The Giants scored nine runs in the four games, yet they are moving on.

“When you put runners on base, good things happen,” Panik said. Then, sounding wise beyond his years, he added, “In a playoff game, you’ve got to score runs. It doesn’t matter how.”

Henry Schulman is a San Francisco Chronicle staff writer. E-mail: hschulman@sfchronicle.com Twitter: @hankschulman

Giants vs. Nationals

Giants win series 3-1

Game 1: Giants 3, Washington 2

Game 2: Giants 2, Washington 1 (18)

Game 3: Washington 4, Giants 1

Game 4: Giants 3, Washington 2

NLCS schedule

Saturday: at Cardinals, 5:07 p.m. (Fox)

Sunday: at Cardinals, TBA (FS1)

Tuesday: at Giants, TBA (FS1)

Oct. 15: at Giants, TBA (FS1)

Oct. 16: at Giants, TBA (FS1)*

Oct. 18: at Cardinals, TBA (Fox)*

Oct. 19: at Cardinals, TBA (FS1)*