The Nationals were 2-1 behind heading to the eighth inning, which was where Tyler Moore pinch-hit a two-run single, allowing Michael Morse and Ian Desmond to score and earn the win.
Monday will see the Cardinals have the chance to strike back in the second game of the five-game series.
The Oakland Athletics urgently need to make home advantage count after sliding 2-0 behind in their American League play-off against the Detroit Tigers.
The A's finished the regular season with six straight wins but back-to-back losses in Detroit have jolted their title hopes.
Detroit won the second game 5-4, with Don Kelly playing the key role at the game's denouement.
He firstly brought the score level at 4-4 with a run on a wild pitch from Ryan Cook, then drove in the winning run with a sacrifice fly off Grant Balfour, with Omar Infante the man to score.
The series now switches to Oakland, with the home side needing to win three straight games. If Detroit have their way, the series will end when the teams next play, on Tuesday.
The New York Yankees made an ideal start to their AL series against the Baltimore Orioles, winning 7-2 at Oriole Park.
The Yankees went into the ninth inning tied at 2-2 but a spree was started by Russell Martin's homer off Jim Johnson to left field, followed by Ichiro Suzuki singling in Eduardo Nunez, Robinson Cano doubling in runs for Derek Jeter and Suzuki, and Nick Swisher's sacrifice fly allowing Robinson Cano to score.
They re-engage in play-off action on Monday, with Baltimore looking to give themselves something to take to New York.
A majestic pitching performance from Bronson Arroyo, who allowed only one hit over seven innings, spurred the Cincinnati Reds to a 9-0 victory over the San Francisco Giants.
That gave the Reds a 2-0 lead from their two games in San Francisco, and the teams meet again in Cincinnati on Tuesday, when a place in the NL Championship series will be beckoning for the hosts.
Ryan Ludwick homered to centre field at the top of the second inning, and the visitors just kept building on their lead as Arroyo kept the Giants scoreless.