Rosario cracked a two-run homer and added a run-scoring single while Dexter Fowler went 3-for-5 with two RBI and three runs scored as the Rockies scored 10 times against the Giants for a second straight game.
Tyler Chatwood (2-0) notched the victory, yielding one run on seven hits over 5 2/3 innings. He overcame four walks while striking out four.
Giants starter Tim Lincecum (3-3) was roughed up for six runs on seven hits over five full innings.
Brandon Crawford went 2-for-3 with an RBI for San Francisco, which fell for the fourth time in five contests.