Chatwood (2-2) scattered three hits over five scoreless frames to earn the victory, issuing two walks and striking out two.
Dexter Fowler, Tyler Colvin and Chris Nelson drove in runs for Colorado.
San Francisco's Tim Lincecum (6-12) was saddled with the loss, surrendering three runs on six hits over seven innings.
The Giants fell into a first-place tie with the Los Angeles Dodgers atop the National League West with the loss.
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