Bumgarner (15-10) overcame five walks and four hits in breaking a personal four-start winless streak, striking out six en route to the victory.
Hunter Pence's RBI single in the sixth inning against Guillermo Moscoso (3-2) broke a 1-1 tie as National League West-leading San Francisco took the opener of a four-game set.
Josh Rutledge provided the only RBI for the Rockies.
Wisconsin business offering 'therapeutic cuddling' forced to close
Exploding whale video goes viral on Internet