Greinke, unscored upon in his first two spring training outings, was effective again, allowing one run and two hits in four innings.
The 2009 AL Cy Young Award winner struck out three and retired the side in order in three innings, throwing 41 of his 61 pitches for strikes.
"Control kind of got a little better, my arm really didn't get tired so much. I probably could have gone like a regular game," Greinke said. "The first two games were a little bit of luck, and this one was just good pitching."
Buehrle, Chicago's projected Opening Day starter, gave up three runs and nine hits in four innings in his second start of the spring. The runs were the first Buehrle has allowed.
"He just tried to get his innings up and he's trying to get ready for the season," White Sox manager Ozzie Guillen said. "I just worry about him getting back in good condition for opening day and make sure he does everything he can do to be the first guy out there for us."
Both pitchers worked quickly, though they did allow a few hard-hit balls. Buehrle allowed a run in the third inning and two in the fourth.
De Aza, an outfielder with only 67 major league games of experience who is trying to win a spot on the final roster, continued his strong spring. De Aza didn't play in 2008 because of a bad left ankle sprain and missed four months with a sprained right ankle in 2007. On Monday, he raised his hitting streak to six games and is batting .462 with seven RBIs.
But he might not be in Guillen's plans.
"My 25 guys is already in my house, printing," Guillen said. "I think my roster is already set. In my mind I've got an idea of what kind of ballclub we're going to have."
White Sox closer Bobby Jenks was expected to pitch Monday night but instead threw a bullpen session earlier in the day. Jenks has struggled so far in spring training, having allowed seven earned runs and three walks in his first two appearances. Jenks has an ERA of 37.80. It's not clear if the strained calf he dealt with late last season remains an issue. ... The White Sox committed three errors in the game.