Pitching a gem, Zito came out only after giving up a one-out walk to Darwin Barney in the ninth inning. Sergio Romo retired the last two batters to lock down his second save and San Francisco's sixth win in seven games.
Zito (5-2) allowed just four hits and two walks, striking out five in another good performance by a Giants starting pitcher. The team also won the first two games of the four-game series behind stellar outings by Madison Bumgarner and Matt Cain.
Bumgarner took a shutout into the ninth inning Friday in a 4-3 win and Cain went eight-plus innings in Saturday's 2-1 victory.
"It inspires each of us to go out there and do it the next day," Zito said of the strong starts.
Chicago starter Travis Wood, meanwhile, was an unlucky loser.
Wood (0-2) was perfect through three innings and didn't surrender a hit until the fifth, when the Giants scored their first run. The 25-year-old lefty went seven innings, giving up just three hits and two walks with seven strikeouts.
Both teams had just four hits, but the Cubs saw their road losing streak reach 10 games.
"Zito's had his issues in the past, but that doesn't look like the same guy," said Cubs catcher Koyie Hill. "He's keeping the ball down and was competitive with all his pitches and it makes it tough on us, especially in a ballpark where it's not very hitter-friendly to begin with."
Zito threw 61 of his 96 pitches for strikes for his 150th career win and fourth in his last five starts. He nearly had two shutouts in 11 starts this season after going almost nine years without one.
In his first outing of the season, on April 9 after he had made a start in the minors while trying to overcome a tough spring, Zito threw a four-hit shutout against the Rockies in Denver.
It was his first shutout in almost nine years, since April 19, 2003, when he was pitching for the Oakland Athletics and coming off winning the AL Cy Young Award the previous year.
Bruce Bochy said Zito's outing Sunday was up there with his best of the year so far.
"What a terrific job he did. He had all his pitches going, threw strikes, threw any pitches at any time and stayed in command," said Bochy.
Wood didn't allow a baserunner until hitting former Cub Ryan Theriot in the fourth inning, but Theriot was erased on a double play. So Wood faced the minimum until Angel Pagan laced a one-out double in the fifth.
Joaquin Arias followed two batters later with a two-out single through the right side that scored Pagan for a 1-0 lead. The throw from Reed Johnson beat Pagan to the plate, but Hill dropped the ball.
That was all until the eighth inning, when Gregor Blanco scored all the way from first base on Melky Cabrera's single when the throw from Alfonso Soriano in left field went to second.
Romo appeared to injure himself on the last play of the game, a ground ball he fielded in front of the rubber. "He's getting looked at," Bochy said. "We think he's fine."...The Cubs have lost all three games in this series after sweeping the Padres in a three-game set. That came on the heels of their 12- game losing streak.
For more on the Giants head over to McCovey Chronicles.