All five of the Giants' hits were singles, but took advantage of two opportunities when they scored on a double-play in the seventh and a sacrifice fly an inning later.
Once agains the Giants received excellent pitching. Right-hand starter Madison Bumgarner shut out Detroit over seven innings, and struck out eight while only allowing two hits and two walks.
Santiago Casilla held the game while Sergio Romo pitched the ninth to get the save.
The Giants have now won five games in a row, and by a combined score of 30-4.
The Tigers wasted an strong outing from Doug Fister. The lanky right-hander conceded just one earned run in six innings.
The normally reliable middle of the order struggled for Jim Leyland's squad. Miguel Cabrera, Prince Fielder, Delmon Young, and Jhonny Peralta combined for just one single and a walk over 10 at-bats.
The series shifts back to Detroit for Game Three on Saturday.
"It's the best of seven, we're up 2‑0," Giants manager Bruce Bochy told reporters. "That's the way we have to look at it. It's the best of seven. It's great to get off to a good start.
"We're heading to Detroit and playing in their ballpark, and you keep pushing. That's what you do at this point. We don't, believe me, take anything for granted," he added.
"You go out there and you play hard every game, and two days from now is our biggest game, and that's how we approach it."