Harang (4-3) limited the Rockies to four hits and three walks. He struck out six for the National League West-leading Dodgers, who ended their longest losing streak in nearly two years.
Elian Herrera's two-run single in the second inning put Los Angeles ahead to stay and Andre Ethier added two RBI.
Bobby Abreu socked a solo homer for the Dodgers, who evened their three-game series against the Rockies.
Colorado starter Juan Nicasio (2-3) allowed three runs (two earned) on four hits before leaving the game with a strained knee after 1 2/3 innings.
Michael Cuddyer and Wilin Rosario drove in runs for the Rockies, whose five-game winning streak came to an end.