Rosario had three of Colorado's 14 hits, including a solo home run, and scored two runs.
The win gave Colorado its eighth victory in their last 10 games and consigned the Dodger to their third consecutive loss.
Andrew Brown also had three hits and an RBI for the Rockies, who jumped out to a 4-0 lead in the first inning. Dodgers outfielder Matt Kemp left the game after crashing into the outfield wall in the same inning.
Tyler Chatwood (4-3) earned the victory with two runs on five hits in five innings.
Chris Capuano (11-10) took the loss after giving up six runs and 10 hits over six innings. Hanley Ramirez hit a solo home run in the ninth for Los Angeles and Andre Ethier had two hits and scored a run.