Bumgarner (6-4) gave up two hits in seven innings. He retired the first 14 men he faced before walking B.J. Upton in the fifth and did not give up a hit until Chris Johnson came through with a leadoff single in the sixth.
San Francisco produced the only run it needed on the fourth pitch of the game when Gregor Blanco homered to right. Blanco also had an RBI single in the second.
Buster Posey scored twice and doubled home a run in the third.
The Giants put together their second shutout in a row, having downed Pittsburgh 10-0 on Thursday.
Kris Medley (3-7) was charged with the loss, giving up four runs on nine hits in six innings.