The Cardinals became the first team in the majors this year to win 40 games.
St. Louis put together two big innings to take a 7-0 lead and make things easy for Adam Wainwright (9-3). He gave up two runs on seven hits with seven strikeouts over seven innings.
The Cardinals scored three times in the fourth with Freese, Jay and Kozma all delivering an RBI single.
Jay doubled home one run and Kozma doubled home two more during a four-run sixth and Freese contributed his own RBI double in the seventh.
St. Louis came up with 16 hits, six of them off Cincinnati starter and loser Mike Leake (5-3). Leake went five innings while giving up three runs.