Peavy allowed two hits, walked one and struck out three.
"I was able to limit the damage to two runs and leave Buster on third," Graveman said. "Then I was able to settle in. Overall it went well and I'm ready for the season."
Graveman made the changeup a priority this spring and he feels comfortable throwing it in any count.
"I got a couple of ground balls with it, a couple of broken bats," he said. "Even behind in the count it was a good pitch."
Graveman was also excited about getting a chance to pitch in the Bay Area before the season opener.
"The moisture in the air is good for guys who throw sinkers and sliders," he said. "You could see pitches shaping up better here. It was great to get a chance to pitch here before the season."
Giants: RHP Jake Peavy had his best outing of spring training but still did not emphasize results.
"It's nice to be in a different environment," Peavy said. "It did feel more like a regular season game. You want the results but it's more about having comfortability on the mound. It was nice to get some outs but I don't know how imperative it was for results."
Peavy used all his pitches, including a changeup on the game's second pitch to Coco Crisp.
"It's all about pitchability," he said. "We used everything from the get-go. The first three innings I pitched to get outs and then worked on other stuff. I felt like I was ready."
Peavy, who carried a hefty 7.43 ERA into the contest, said results can be misleading. Peavy allowed 19 runs in 23 innings in Arizona.
"I know the biggest question coming out of camp was our pitching," he said. "You can't read into it like that, especially with guys who know they are in the rotation. Everybody is working on things. That being said, it was fun to see us put together some quality starts."
Giants: C Andrew Susac (sore right wrist) was optioned to Triple-A Sacramento, where he will continue to rehab.
Athletics: LHP Felix Doubront starts Saturday's game in Oakland against the San Francisco Giants.
Giants: RHP Matt Cain starts against the A's.