The St. Louis win eliminated the Cincinnati Reds from the division race and the Cardinals have a three-game lead over the Pittsburgh Pirates with three games to play. The Reds and Pirates both lost Wednesday.
St. Louis wraps up the regular season at home this weekend against the Chicago Cubs. The Pirates finish their regular season with a three-game set in Cincinnati.
The Nationals were swept in the series, and were eliminated from playoff contention Monday. Washington, with five hits Wednesday and just Tuesday, scored four runs on 13 hits in the series.
Miller (15-9) surrendered four of those hits, including an RBI single by Bryce Harper in the first inning. Miller walked three and struck out three in six innings.
The Cardinals tied the score in the third when Daniel Descalso doubled, advanced on a Miller sacrifice and scored on a groundout. Matt Holliday was hit by a pitch to open the fourth and Matt Adams doubled him to third. Yadier Molina put St. Louis ahead 3-1 with a single to center.
The Cardinals made it 4-1 in the sixth when Adams hit his 17th home run of the season.
All of the St. Louis runs came against Jordan Zimmermann (19-9), who was seeking to be the National League's first 20 game winner this season. He gave up six hits and struck out two in a seven-inning outing.
Justin Bieber crashes Drake Bell's album release party
Rosie O'Donnell unveils nearly 50-pound weight loss