De La Rosa (1-0), making his first start of the season, struck out nine and walked only one. He threw 97 pitches.
Colorado broke the game open with a four-run seventh that featured a three-run homer from Clint Barmes. Ian Stewart drove in two runs for the Rockies, who lost two out of three to open the season in Milwaukee.
San Diego has cropped three of its first four games.
The loss went to Clayton Richard (0-1), who allowed three runs on seven hits in seven innings.
De La Rosa retired the first eight batters he faced and did not give up a hit until Chase Headley singled in the fourth.
It was the 18th home opener for the Rockies and they have won 11 of them.