Latos (14-5) retired 21 of the final 22 batters he faced in notching his fourth career complete game, allowing two runs. The right-hander issued just one walk and struck out two.
Shin-Soo Choo belted a two-run homer and Joey Votto added his 21st round-tripper of the season for the Reds, who opened a key four-game National League Central series with a win.
Third-place Cincinnati came into the contest trailing division leader Pittsburgh by three games, while the Cardinals temporarily fell out of first by a half-game with the loss.
St. Louis starter Adam Wainwright (15-9) was roughed up for six runs on 10 hits over 10 innings.
Matt Carpenter and Matt Holliday each supplied an RBI for the Cards.