Matt Kemp clubbed a three-run shot and Aaron Miles added a two-run homer for the Dodgers, who won for the fourth time in six games thanks to their first double-digit performance since June 27 at Minnesota.
Justin Sellers and Jamey Carroll each contributed three hits for Los Angeles.
Clayton Kershaw (16-5) turned in six scoreless innings, fanning eight and walking two while scattering six hits.
The left-hander won for the eighth time in his last nine starts and turned in consecutive scoreless outings for the first time all season. He's tied with Ian Kennedy of Arizona for the NL lead in wins.
Ryan Theriot and Jon Jay drove in late runs for the Cardinals, who have lost six of their last eight and tumbled 10 games behind the first-place Brewers in the NL Central. Milwaukee pounded Pittsburgh, 11-4, earlier Tuesday.
Kyle Lohse (11-8) departed after three innings, charged in defeat for eight hits and a season-high eight runs