Hudson allowed one run and scattered seven hits in his fifth Cactus League start for his new team. The 38-year-old right-hander walked one, struck out two and gave up a second-inning homer to Alejandro De Aza.
''It was definitely a step in the right direction for me,'' Hudson said. ''Definitely found the strike zone a lot better than I had been the previous couple starts. That's what I was wanting to do coming in, try to find the strike zone, work ahead of hitters and get a little deeper into games. It was a really good work day.''
Juan Perez hit a three-run homer in the sixth to give San Francisco a 4-1 lead. Posey had two RBIs.
Posey, an All-Star catcher and the 2012 NL MVP, said Hudson ''looked good'' on the mound.
''He had a game plan coming in to attack the strike zone and I think he did that,'' Posey said. ''We've gotten on the same page pretty quick and the more that we work together, the better we'll get.''
Giants: In addition to shutting down the White Sox lineup, Hudson had two singles at the plate and was all smiles in the clubhouse after manager Bruce Bochy removed him for Jeremy Affeldt.
''I'm just swinging the bat, they're hitting it for me - trust me. I'll probably go 0 for my first 10 games,'' Hudson said, laughing. ''They did tell me there was a batting title for spring training, so I'm shooting for it.''
White Sox: Felipe Paulino pitched 5 1-3 innings, giving up five runs on eight hits and four walks - including the three-run homer by Perez. Paulino was removed a batter later for reliever Mitchell Boggs.
Giants: Outfielders Angel Pagan (back) and Michael Morse (calf) were in the lineup Friday night against Oakland, but received the day off Saturday. ... Second baseman Marco Scutaro received his second epidural shot of the spring Thursday to relieve the pain in his lower back.
White Sox: Catcher Tyler Flowers said he felt good Saturday morning after he was taken out of Friday's game against the Chicago Cubs with leg cramps.
''It was just a little cramp, and I've been a little sick lately so that didn't help things,'' Flowers said. ''It's nothing to worry about, it was just a little cramp, and I was done after that at-bat anyway. I just couldn't get it to go away and there's no point to try and push through it in that situation.''
Flowers was removed in the middle of an at-bat after he swung through a 1-1 pitch from Cubs reliever Alberto Cabrera in the sixth inning. Flowers was not in the starting lineup Saturday against the Giants, but did enter for Rule 5 selection Adrian Nieto in the top of the eighth inning.
UP FOR GRABS
White Sox prospect Matt Davidson is competing with Conor Gillaspie for the starting job at third base. The 22-year-old Davidson said he ''hasn't heard anything'' and ''it's been pretty quiet'' in terms of which way manager Robin Ventura is leaning.
''I've been working hard to get ready for the season,'' Davidson said. ''That's obviously the goal, to be in the big leagues. I have a great opportunity here.''
Davidson went 2 for 4, raising his batting average to .304 in 17 games this spring with two home runs, two doubles and six RBIs.
POSEY AT FIRST
Posey said he will get a start at first base sometime before camp breaks Wednesday in an effort to get him time at the position for a backup role.
Brandon Belt is the only true first baseman in big league camp after the Giants reassigned Mark Minicozzi to minor league camp Friday.
Posey has started 77 regular-season games at first base since 2010, mostly to get his bat in the lineup and give his legs a rest.
Retired U.S. Marine Tom Pagliuco received a standing ovation from 11,524 fans before and after he threw out the ceremonial first pitch.
The former Chicago Police detective served in Vietnam from 1967-68 and was awarded the Bronze Star in addition to three Purple Heart medals. He began working security for the White Sox at Comiskey Park in 1990 and is now the head of security at Camelback Ranch in Glendale.