De La Rosa (14-6) struggled at times but held the Marlins to three runs on five hits. He walked three and struck out three.
Adam Ottavino, Josh Outman, Wilton Lopez and Matt Belisle combined for three innings of scoreless relief and Rex Brothers recorded his 13th save as Colorado claimed the rubber match of a three-game series.
Nelson Arenado's run-scoring double in the sixth inning broke a 3-3 tie and proved to be the game's key hit.
Arenado and Ryan Wheeler each went 2-for-4 with an RBI in the victory.
Miami's Jacob Turner (3-5) was hung with the loss, surrendering four runs (three earned) on six hits over 5 2/3 innings.
Justin Ruggiano pounded a solo homer and finished with two RBI for the Marlins.
2014: The Year in Music [PHOTOS]