Vogelsong (1-0) scattered five hits over 5 2/3 innings to earn the victory, using two double plays to overcome four walks. The right-hander struck out three.
San Francisco blanked hard-hitting Detroit for the second straight game and now are in a position to win their second World Series title in three years with another victory in Sunday's Game 4.
The Giants scored both of their runs in the second inning when Hunter Pence scored on a Gregor Blanco triple, and Blanco came home on Brandon Crawford's run-producing single.
The Tigers' Anibal Sanchez (0-1) pitched well in defeat, allowing just the two runs on six hits over seven innings. He walked one and struck out eight.