Kolten Wong had three hits and drove in two runs and Jeremy Hazelbaker hit a two-run homer for St. Louis. The Cardinals have won four of five and lead the Marlins by one game in the NL wild-card standings.
Marlins outfielder Ichiro Suzuki went 0 for 4 to remain at 2,998 career hits.
Martin Prado homered and drove in three runs, and Marcell Ozuna also homered for the Marlins.
Mike Leake (8-8) won despite giving up six runs and seven hits in five innings.
Jose Urena (1-3) allowed eight runs in 4 1-3 innings in what is expected to be his final start in the Marlins' rotation after Miami acquired starters Andrew Cashner and Colin Rea from San Diego earlier in the day.
