"They keep us in the ball game and some timely hits from this kid, and the rest of the guys coming off the bench, that's really been the formula."
The Nationals, who had never come close to making the playoffs since moving from Montreal for the 2005 season, overcame a wild start by 21-game winner Gio Gonzalez. They limited the Cardinals to just three hits.
"All the credit in the world goes to the bullpen," Gonzalez said. "I've been saying it all year. The reason why we've been so successful is these guys come in and shut it down."
Rookie reliever Ryan Mattheus needed just two pitches to bail out the Nationals in the seventh with St. Louis ahead by 2-1. Moore, another rookie, put them ahead soon after that. Tyler Clippard worked around an error in the eighth, and Drew Storen saved it with a 1-2-3 ninth.
The NL East champion Nationals led the majors with 98 wins this season, and brought postseason baseball to Washington for the first time since 1933. The Nats go for a two-games-to-none series lead Monday when Jordan Zimmermann opposes Jaime Garcia.
"This team is not hanging our heads," St. Louis starter Adam Wainwright said. "We can come back and win this easily."
The Cardinals made it to the best-of-five division series by beating Atlanta in the wild-card matchup Friday. But St. Louis wasted a 10-strikeout gem by Wainwright, failing to capitalize enough on Gonzalez's career-high-tying seven walks and frustrating its towel-waving fans.
Mattheus diffused a bases-loaded, none-out threat in the seventh, getting cleanup man Allen Craig to ground into a forceout at the plate and then inducing a double-play grounder from Yadier Molina. Craig led the National League with a .400 average with runners in scoring position, and Molina batted .321 in those situations.
"It was a big moment," Mattheus said. "It gave us life. The guys said, 'Hey, we can win this ballgame.' "
A standing-room crowd of 47,078, among the largest at seven-year-old Busch Stadium, bundled up for a game that began in 54-degree chill and featured kaleidoscope late-afternoon shadows that bedeviled hitters for several innings.
"It was pretty bad, but you have to make adjustments, and that's what I did," Molina said. "But what are you going to do? Quit? No."
Third-place hitter Matt Holliday chimed in his complaints about facing Gonzalez: "He's hard to hit when you can see well and even harder when you can't."
Rookie shortstop Pete Kozma misplayed Michael Morse's grounder for an error to open the eighth and set up the Nationals' go-ahead rally.
Nationals rightfielder Jayson Werth robbed Daniel Descalso of a two-run homer with a leaping catch to keep it at 2-1 in the sixth.
Descalso had a fielding gem of his own in the seventh, ranging far to his left to glove Bryce Harper's grounder and then throwing him out by a few steps.
Gonzalez allowed just one hit in five innings, on David Freese's full-count bouncer between third and short to start the fourth.