Miami put two runners on base in each of the first two innings and the Marlins were retired in order just once by De La Rosa (10-5).
Nolan Arenado singled in Colorado's first run in the second inning and DJ LeMahieu delivered a sacrifice fly in the fifth.
The Rockies used five relievers, who combined to give up a run on five hits over the final three innings. Rex Brothers issued a two-out walk in the ninth on his way to his sixth save.
Jacob Turner (3-3) took the loss despite allowing only two runs on six hits over six innings.