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, 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 2-0 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 wasted a 10-strikeout gem by Wainwright, failing to capitalize enough on Gonzalez' career-high-tying seven walks and frustrating their towel-waving fans. Wainwright became the first Cardinal to reach double digits in strikeouts since Bob Gibson also fanned 10 to beat the Tigers in Game 4 of the 1968 World Series.
Mattheus diffused a bases-loaded, no-out threat in the seventh, getting cleanup man Allen Craig to ground into a forceout at the plate and then inducing a doubleplay grounder from Yadier Molina. Craig led the NL 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.' "
In the other game: *
At San Francisco, Bronson Arroyo held the Giants to one hit in seven innings and combined with two relievers on a two-hit shutout as Cincinnati posted a 9-0 win to take a 2-0 lead in the series.
Ryan Ludwick got the scoring started with a solo homer off Giants starter Madison Bumgarner in the second inning, and the Reds increased the lead to 4-0 with three in the fourth inning. Jay Bruce's two-run double triggered Cincinnati's five-run eighth inning that broke the game open. Ryan Hanigan drove in three runs with a two-run single in the fourth and an RBI single in the eighth.