Bumgarner (1-0) set down 18 consecutive batters and struck out six before Sergio Romo came in to pitch a perfect ninth inning and earn his first save.
San Francisco hit into four double plays.
Hyun-Jin Ryu (0-1) came up short in his first start since signing a $36 million contract with the Dodgers. The South Korean southpaw was hung with the loss after allowing three runs – one earned – on 10 hits over 6 1/3 innings. Ryu struck out five and did not walk a batter.
Los Angeles was held to two hits. Andre Ethier and Mark Ellis both doubled.