Vogelsong (1-2) benefited from a second-inning home run by Brett Pill in the Giants' third win in their last four outings, while Kershaw (2-1) was tagged with his first loss of the season.
Vogelsong scattered eight hits and walked three over 7 1/3 innings. Santiago Casilla recorded the final out of the game for his sixth save after Javier Lopez snuffed out the Dodgers' threat in the eighth by getting Andre Ethier to hit into a double play with the bases loaded.
Kershaw, who had won his previous 12 decisions at Dodger Stadium, went an efficient eight innings in which he allowed two runs on five hits and a walk. He struck out seven.
James Loney had two hits for the Dodgers and drove in their only run with an RBI double in the second.
Pill had given San Francisco a 2-0 lead in the top of the second with a home run to left field after Buster Posey led off the frame with a single. The homer was the first for the Giants since May 1.