Minor (8-10) walked four, but did not allow a hit until Jordan Pacheco led off the seventh with a single.
Pacheco stole second, but was stranded there and the only other Colorado hit came in the eighth when Josh Rutledge singled off Eric O'Flaherty. Craig Kimbrel came on to get the final out of the eighth and struck out the side in the ninth for his 33rd save.
The lone Atlanta run was an unearned one in the fourth off Alex White (2-8).
With runners on first and second and nobody out, Brian McCann hit a grounder to second base. An out was recorded at second, but the throw by the shortstop Rutledge to first in a bid to complete a double play got away for an error. Chipper Jones came in to score the winning run.