Norichika Aoki added a run-scoring triple to left-center in the second, a drive that continued carrying and landed just out of reach for center fielder Jordan Danks. Aoki finished with two hits, while Rickie Weeks scored two runs after being hit by a pitch and drawing a walk in two at-bats.
Peavy allowed three runs on four hits over two innings, striking out two and not issuing a walk. Of most importance for the right-hander, beset by injuries since arriving with the White Sox, was that he felt great on the mound.
"I did, I did, I really did. I can't help but have a big smile on my face," Peavy said. "I know I gave up a few runs, but it's fun to be out there. I feel good, and absolutely nothing in my body is hurting. And it was fun to get my work in."
Marco Estrada worked two scoreless innings for the Brewers, striking out one and giving up three hits. Closer John Axford and Kameron Loe also pitched one scoreless frame apiece.
Brent Morel knocked out two hits for the White Sox, while Jared Mitchell came up with his first Cactus League home run. Mitchell's two-run shot was part of a three-run fifth inning.
White Sox up next: Much of the White Sox regular lineup will be in Surprise, Ariz., for the Cactus League game against hard-throwing Neftali Feliz and the Rangers, with a 2:05 p.m. CT first pitch. But pitchers such as Gavin Floyd, Addison Reed and Will Ohman are scheduled to pitch in the morning B game, also in Surprise against the Rangers. Look for Alejandro De Aza in center, Morel at third, Dayan Viciedo in left, Adam Dunn at first and Gordon Beckham at second, hitting seventh, in the main afternoon contest, with Hector Santiago on the mound.
Brewers up next: Zack Greinke will make his first Cactus League start on Thursday at 2:05 p.m. CT, when the Brewers return home to Maryvale Baseball Park to host the Reds. Greinke, who worked around three hits in three scoreless Sunday in relief of Randy Wolf, is among a slew of Brewers pitchers working on a cut fastball this spring. He threw four of them against the Giants and was happy with three, a sufficient ratio, Greinke said, to continue tinkering with the popular pitch. Look for first baseman Mat Gamel and third baseman Aramis Ramirez to return to action after getting Thursday off.