Zito (6-5) didn't allow a runner to reach third in the gem, stifling the Dodgers on three hits while walking three and striking out four.
The left-hander broke a personal three-game losing streak while tossing 62 of his 109 pitches for strikes, as the Giants opened a three-game series against their National League West rivals with a victory.
Sandoval's two-run double highlighted a four-run first inning for San Francisco and later added a sacrifice fly to cap a three-run second as the second-place Giants sliced the Dodgers' division lead to two games.
Angel Pagan and Hector Sanchez each added two hits and two RBI for San Francisco.
Los Angeles starter Nathan Eovaldi (0-4) was battered for eight runs on 10 hits over five innings.