A rare command lapse cost Brewers starter Kyle Lohse, who had not walked or hit a batter in his first eight Cactus League innings, before running into trouble in the fourth. He began the inning with a walk, a hit batsman and another walk before Davidson, Chicago's third baseman, pulled a 3-and-0 pitch over third base for a two-run double.
Hector Gimenez added a sacrifice fly in the inning and Ramirez an RBI single, knocking Lohse from the game. He was charged with five earned runs on seven hits in 3 2/3 innings, with two strikeouts and two walks.
Lohse hinted afterward that he was having trouble with the Maryvale mound.
"I don't want to complain," Lohse said. "I just got out of kilter for a minute and couldn't find everything that I needed. But I got in [the work] that I needed to."
Brewers closer Jim Henderson surrendered four more runs on four hits and a walk in the seventh. Ramirez and Adam Dunn delivered RBI doubles before Richmond came off the bench to hit a two-run home run.
White Sox starter Felipe Paulino walked three batters in five innings but allowed only two hits and no runs, with four strikeouts. He was in trouble after Brewers shortstop Jean Segura lined an opposite-field triple with one out in the third inning, but Paulino retired Ryan Braun on an infield pop-up and caught Aramis Ramirez looking to escape without allowing a run.
"I feel like every time I come in here, everything's coming together right now," said Paulino, who incorporated a cut fastball into his arsenal on Monday for the first time in his career. "I improved today, just to throw five innings. That's what [pitching coach Don] Cooper and I are looking for -- to go deep in the game."
Up next: After a trip to Maryvale Baseball Park on Monday, the White Sox return to Camelback Ranch on Tuesday for a visit from the A's. Left-hander Jose Quintana is scheduled to to start against Oakland righty Jesse Chavez. Matt Lindstrom, Ronald Belisario, David Purcey, Eric Surkamp and Maikel Cleto are also expected to pitch. The game will be broadcast live on MLB.TV and on CSN Chicago at 3:05 p.m. CT.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.