Schierholtz hit a two-run blast in the fourth inning to extend the Giants' lead to 4-0 and San Francisco hung on to take the first contest in a three-game series against their Western Division rivals.
Pablo Sandoval contributed two hits and drove in a run for the Giants, who benefited from 5 2/3 effective innings by Bumgarner. The rookie hurler allowed only one unearned run on six hits, walking two and striking out three.
Brian Wilson tossed a scoreless ninth for his 26th save despite loading the bases with two outs.
Dodgers starter James McDonald (0-1) was roughed up for four runs on nine hits in five innings.
Rafael Furcal homered and stroked three hits and Matt Kemp went 3-for-4 with an RBI for Los Angeles.