The other big hit for St. Louis was Allen Craig's two-run double in the third.
Miller (3-1) struck out eight in 6 2-3 innings, allowing two runs and four hits.
All the Cardinals' runs came against Dan Haren (1-3), who gave up three runs and six hits in five-plus innings.
Edward Mujica pitched a 1-2-3 ninth for his second save. The Cardinals have alternated wins and losses over their last nine games.
Washington has lost seven of 10.
The last time these teams played in Washington was Oct. 12, in Game 5 of an NLDS, when the Nationals led 6-0 after three innings and were still ahead 7-5 with two outs in the top of the ninth. But with then-closer Drew Storen on the mound, Washington allowed St. Louis to rally for four runs and a 9-7 victory that ended the Nationals' season.
The last two runs scored on a hit by Cardinals shortstop Pete Kozma, who was booed during pregame introductions Monday and again when his name was announced before his first plate appearance, in the third inning.
He singled to right in that at-bat, the ball landing not too far from where his go-ahead hit landed in October. This time, it was part of a two-run inning, with Kozma and Matt Carpenter coming home on Craig's double off the wall for a 2-0 lead.
Storen appeared in Monday's game, too, coming in to throw the ninth with Washington down by a run. And wouldn't you know it? The leadoff hitter was Kozma, although this time he struck out looking. Next up for Storen was pinch-hitter Daniel Descalso, whose two-run hit tied Game 5. Storen got him to pop out to third Monday, part of a 1-2-3 inning.
Jayson Werth led off the Washington fourth by reaching when Kozma went deep into the hole and made a leaping throw across his body that Craig bobbled at first base. Werth was credited with a hit. He came around to score and make it 2-1 on Ian Desmond's double over the head of center fielder Jon Jay.
Anthony Rendon, called up from Double-A Harrisburg over the weekend to fill in while third baseman Ryan Zimmerman is on the disabled list, followed with his first major league hit and RBI - doubling to right-center on a 3-2 fastball. That brought around Desmond, making it 2-all.
Rendon, the No. 6 overall pick in the 2011 draft, made his debut for the Nationals on Sunday at the New York Mets, going 0 for 4 with two strikeouts and an error. He joked before Monday's game: ''I don't think you can get any worse; I don't think you can go negative in the batting average.''
His parents had tried to travel from Houston to New York for his first game, but a problem with the airline scuttled those plans. Rendon said they made it to Washington on Sunday night and were going to be at Nationals Park, along with his girlfriend, his brother and a buddy.
In the sixth, things went wrong for Haren - and well for the Cardinals - in the span of three pitches. And Kozma, once more, figured in it, with a bit of a flashback to October.
Haren plunked the inning's first batter, Matt Holliday, and then served up first-pitch singles to Carlos Beltran and Molina, putting St. Louis ahead 3-2. Haren then walked David Freese, loading the bases with no outs, and was done.
In came righty reliever Craig Stammen, who got Jay to ground into a 3-2-3 double play. After intentionally walking Kozma ahead of the pitcher's spot - something some fans surely wished the Nationals had done six months earlier - Stammen struck out Miller to end the inning.
NOTES: Cardinals 1B Matt Adams was removed from the lineup after feeling soreness in his right side during batting practice. ... Nationals C Wilson Ramos, on the DL since April 14 with an injured left hamstring, is expected to be back when his required 15 days away are up. Manager Davey Johnson said Ramos probably will go to extended spring training in Viera, Fla., to get some at-bats before returning to the club. ... Washington closer Rafael Soriano was away from the team because his wife gave birth.
Link to box score: St. Louis 3 at Washington 2
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