Kim (5-2) allowed four runs on five hits, mixing in two walks with four strikeouts as he improved to 3-0 over his last four starts. Cory Sullivan and Todd Helton each drove in a run for the Rockies.
Brian Fuentes recorded his 27th save of the season.
Edwin Jackson (1-2) suffered the loss for the Dodgers, as he didn't last past the second inning when he was battered for six runs -- five earned -- on three hits and three walks.
For the Dodgers, Jayson Werth went 2-for-3 with an RBI and Jose Cruz, Jr. also drove in a run.
The Rockies enjoyed the six-run advantage until the home club erupted for four runs in the bottom of the fourth inning.