Burris led off the inning with a single off Athletics closer Brian Fuentes (1-5) and took second on a sacrifice bunt by Andres Torres. After an intentional walk to Freddy Sanchez, Fuentes served up the game-winning RBI single to Huff.
The Giants won their third straight game. The A's have lost three straight.
Mark Ellis had two of Oakland's five hits.
San Francisco starter Ryan Vogelsong went six innings, allowing one run on four hits with two walks and five strikeouts.
Trevor Cahill started for Oakland and allowed one run on one hit, with two walks and six strikeouts in six innings.
Javier Lopez (2-0) got the win in relief for San Francisco.