Zito will look to help the Giants win their 10th straight at home versus the Oakland Athletics on Friday night when the Bay Area rivals open a three-game series.
In the second-to-last year of a seven-year, $126 million contract, Zito (2-1, 2.53 ERA) has never finished with a winning record for the Giants nor had an ERA lower than 4.03.
However, the left-hander hasn't given up more than three earned runs in seven start this season, including at Arizona on Sunday when he allowed three runs and struck out five in six innings of a 7-3 win.
"It's been good, contributing the best I can this year," he said. "I don't feel like I've made any kind of statement and I won't until the year is over. I've got a lot of work to do. I'm off to a decent start but I can't take anything for granted."
It also marked some rare offensive support for Zito, who was winless since his first start. The Giants scored three or fewer runs in each of his previous five outings.
Building on the victory Friday could be difficult. Zito snapped a four-game losing streak against his former team in 2010 to improve to 1-4 with a 7.24 ERA versus Oakland.
The Giants (19-19) split a pair of two-game sets this week with Colorado and St. Louis, avoiding a third straight loss with a 7-5 win over the Cardinals on Thursday.
While San Francisco has waited a long time for Zito to pay dividends on his contract, the Athletics are seeing early results from Jarrod Parker (1-1, 2.10).
Oakland (20-19) acquired Parker in December from Arizona, and the 23-year-old right-hander has pitched into the sixth in all four starts while surrendering two or fewer runs in each of them. He lasted 5 2-3 innings against Detroit on Sunday, allowing two runs in a 3-1 loss.
Oakland continues a seven-game road trip after splitting a two-game set with Texas. The Athletics won 5-4 in 10 innings Thursday on Kila Ka'aihue's RBI single.
Manager Bob Melvin was ejected in the sixth on a disputed call that allowed the Rangers to take the lead.
"I thought it was terrific," Melvin told the Athletics' official website. "We lose a game here (Wednesday) when we didn't play great, and we come back and deal with some adversity and such and get some big hits, and everyone contributes. ... This was as much of a team win as you're going to see."
This series begins in the wake of baseball Commissioner Bud Selig's comments at the quarterly owners meeting Thursday about a potential move by the Athletics.
Oakland is looking to build a new ballpark 40 miles south of the city in San Jose, which is considered part of the Giants' territory. Selig said it's up to Lew Wolff, the A's owner, whether to consider additional sites.
The A's have averaged 1.8 runs during their nine-game skid at AT&T Park.