Zito (7-15) allowed five hits and two walks without a run for his first win since Aug. 2.
Rich Aurilia and Pablo Sandoval also drove in runs for the Giants, who won three of four in the series.
Atlanta starter Jorge Campillo (7-6) gave up five runs on seven hits over 6 2/3 innings. The Braves have lost seven of their last eight games.
The Giants had not won a series in Atlanta since taking two of three May 28-30, 1993, going 0-18 with three splits in series since then.