Dan Straily and three Oakland relievers held the White Sox to three hits.
Straily went 3 1-3 innings, walking three and striking out two. He gave up two hits - one was Matt Davidson's deep fly to left that Yoenis Cespedes misjudged. Cespedes came in on the ball, but it landed well behind him and bounced over the wall for a ground-rule double.
Cespedes' woes weren't over. He struck out three times, and in the sixth he was charged with a three-base error for failing to catch Gordon Beckham's fly to the warning track in left-center. That led to Chicago's first run.
''The wind may have gotten it on the second one,'' A's manager Bob Melvin said of Beckham's drive. ''It looked like he located it, got back to the fence and I think it fooled him on how far it was going. It was traveling a little farther earlier in the game.''
As for the ball hit by Davidson, Melvin said, Cespedes ''never saw it.''
The White Sox's second run also was unearned, as Jake Elmore's error with a runner on third and two outs in the eighth tied it at 2.
Tommy Milone pitched four innings in relief for the A's and was charged with two unearned runs. He gave up just one hit and struck out two. He walked none, hit a batter with a pitch and committed a balk.
White Sox starter Erik Johnson pitched four innings, striking out five. He allowed one run and four hits, walking one.
White Sox: Erik Johnson, who pitched three innings in his first start against Cleveland on Tuesday, threw four on Sunday. He gave up four hits and a run, and struck out five.
''I felt pretty good,'' Johnson said. ''I worked ahead a little more this time around. I got double plays, which helped me out, kept my pitch count down. Overall it was a good outing.''
Daniel Webb worked his first inning in relief for the White Sox. Webb, who is competing for a spot in the bullpen, missed a week for family reasons.
Athletics: Straily was much happier with his second Cactus League outing. In his first against Milwaukee on Tuesday, he walked two, gave up four hits and three runs.
''I felt a lot more in control,'' Straily said of his performance Sunday. ''I was able to focus on what I needed to work on. Some of the stuff that doesn't show up in the box score - throwing the first-pitch curveball for a strike, getting the changeup in the zone, I was very unhappy with the last outing. I was able to fix in my side work and take into the game today.''
Milone, who worked out of the bullpen at the end of last season after beginning in the rotation, gave up just one hit and struck out two, and was charged with the unearned runs. He walked none, hit one batter and committed a balk. Melvin said Milone will have five days before his next appearance.
Jake Elmore's versatility apparently extends to the entertainment world. The infielder, recently claimed off waivers from the White Sox, won the Athletics' first talent show before Sunday's game.
Elmore sang country, rap and pop, while simultaneously changing to appropriate headgear for the genre, and keeping the beat all the while.
''I had no idea that he had that kind of a singing voice,'' Melvin said. ''We'll give him a start tomorrow (Monday) just for that.''
The talent show, which was the idea of new A's reliever Jim Johnson, proved to be a hit.
''I've been to several of those, but I can't remember a time where there was actually talent involved,'' Melvin said. ''Usually, it's more laughing and booing somebody off the stage. This was a very talented group. A pleasant surprise.''
White Sox: LHP Jose Quintana reported no additional pain a day after taking a Gerardo Parra line drive off his left shin. Quintana hopes to make his next scheduled spring start on Thursday. ... Jeff Keppinger, recovering from a sore shoulder, was the Chicago DH on Sunday. Manager Robin Ventura said he wants Keppinger to get at-bats before he returns to the infield later this week.
Athletics: 1B Daric Barton (mild hamstring strain) will miss several days. Melvin said the A's will take it easy with him early in the spring. ... Melvin also said C Derek Norris (back spasms), OF Craig Gentry (back) and RHP Ryan Cook (shoulder inflammation) are making progress. Cook had a bullpen session Sunday. Melvin said Norris hopes to play Tuesday.
After the game, the A's reassigned five players to their minor-league camp, reducing the number in the major league camp to 50. The reassigned players were pitchers Andrew Werner, Jose Flores and Jeremy McBryde, and catchers Dusty Brown and Bruce Maxwell.