De La Rosa (12-6) allowed two runs on eight hits, walking one and striking out six while throwing 73-of-107 pitches for strikes.
The left-hander yielded three or fewer earned runs for the 11th time in 12 starts, lowering his ERA to 3.22.
Matt Belisle hurled a scoreless eighth and Rex Brother turned in a 1-2-3 ninth for his 11th save as the Rockies took the rubber match of a three-game series.
Colorado broke a 1-1 tie in the third inning when Dexter Fowler led off with a single and, one out later, Dickerson lofted a triple into left-centerfield.
Troy Tulowitzki (2-for-4, two RBI) followed by grounding the next pitch up the middle for a 3-1 Colorado lead.
San Diego's Andrew Cashner (8-7) was hung with the loss, surrendering three runs on six hits over seven innings.