"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 D-backs will stay at home and host the Reds on Monday at 1:10 p.m. MT. Brandon McCarthy, Starling Peralta and Tony Sipp are among the Arizona arms slated to pitch while Heath Bell, Willie Bloomquist and David Hernandez join the Team USA roster scheduled to work out for the first time in preparation of the World Baseball Classic at Salt River Fields at 1 p.m MT.
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.