He allowed nine runs, seven hits and two walks, raising his ERA from 16.50 to 30.00.
Quintana, a consistent starter for the White Sox the past two years, said he has no arm problems and that he's not worried.
"I'll be fine when the season starts," he said.
Asked his level of concern, manager Robin Ventura said, "You think about it, definitely, because it's a couple of times now."
"His cutter wasn't as sharp as it's been in the past," Ventura said. "That could be from getting on top and not having as much slide across the plate."
Oakland starter Jesse Chavez improved to 4-0, giving up two runs and six hits in 4 2/3 innings. A's manager Bob Melvin indicated before the game that Chavez and Tommy Milone will be part of the team's starting rotation.
Jordan Danks hit a two-run homer and a solo shot for Chicago, while Conor Gillaspie and Tyler Flowers also hit solo homers. Chicago reliever Ronald Belisario gave up three runs in one inning, raising his ERA to 10.13.
The Associated Press contributed to this report.