Chacin (9-4) held Los Angeles to the one run on six hits and three walks while striking out six.
Cuddyer delivered an RBI single in the first inning and belted a two-run homer in the fifth, providing all of the Rockies' offense.
Ricky Nolasco (6-9) lasted five innings for Los Angeles, allowing three runs on eight hits.
The second-place Dodgers went into the All-Star Game break trailing National League West-leading Arizona by 2 1/2 games.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Charlize Theron not engaged to Sean Penn 'yet'