"I felt better than last time out, for sure," Zito said. "My focus was better, my timing was better and just making more pitches."
The Giants backed Zito with two first-inning runs off D-backs starter Josh Collmenter thanks to an RBI groundout by Buster Posey and a run-scoring single by Francisco Peguero.
Collmenter allowed those two runs on three hits in his two innings of work, while left-hander David Holmberg surrendered another in the third when Gregor Blanco scored on a double-play ball by Hunter Pence.
"I was much better in the second inning, I got a little too much of the plate in the first inning," Collmenter said. "Other than that, I felt pretty good. I was able to get in a bit of a groove in the second and throw some pitches inside. I threw the curveball, too, so it's nice to get a little more trust in that pitch. I like throwing it, so it's good to be able to have situations like this where I can."
Right-hander Steve Edlefsen also tossed a scoreless inning of relief for San Francisco.
The D-backs scored in the fifth inning when John McDonald scored on Willie Bloomquist's groundout off Giants righty Chad Gaudin.
Peguero added a two-run double in the sixth to extend San Francisco's lead.
In his first game against his former team, Cody Ross struck out in his only at-bat before leaving the game as a precaution due to left calf soreness.
Up next: The Giants travel to Camelback Ranch to face the White Sox at 12:05 p.m. PT on Monday. Right-hander Ryan Vogelsong makes his final Cactus League start before leaving camp to join Team USA for the World Baseball Classic. Vogelsong is scheduled to pitch Game 2 for Team USA on March 9 against Italy.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.