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.