Alex Rodriguez singled, walked, was hit by a pitch and lined out to centre field after going 1 for 4 in his season debut Monday. The Yankees lost for the 13th time in 19 games after scoring a run in the ninth against closer Addison Reed.
A-Rod was on deck when Alfonso Soriano struck out to end it with a runner on first.
Reed gave up a single to a pinch-hitter Ichiro Suzuki, who took second on defensive indifference and came around on Brett Gardner's two-out single. But Reed finished for his 27th save in 32 chances.
Adam Dunn singled and scored tying run in the fourth, and Chicago took a 2-1 lead in the sixth when Paul Konerko beat the relay throw on a force to deep third, allowing Alexei Ramirez to score after he led off with a single.
Doubles by Gordon Beckham and Alejandro De Aza in the seventh off Kuroda (10-7) made it a two-run game, sending the White Sox to their second straight win after dropping 10 in a row.
Victimized by poor run support this season, Sale (7-11) got the win after going 1-9 over his previous 11 starts. He allowed five hits and left with one out in the eighth after Rodriguez led off with a single and Robinson Cano lined out.
Nathan Jones struck out Curtis Granderson and Lyle Overbay before the Yankees rallied against Reed.
Kuroda took the loss after going 3-0 in his previous five starts. He gave up three runs and nine hits, but the Yankees came out flat again after getting pounded 8-1 on Monday.
They're hoping Rodriguez can provide a spark and boost their fading playoff hopes, but he's coming off hip surgery and has a long suspension hanging over him after Major League Baseball lowered the hammer on Monday.
Rodriguez, who's appealing the 211-game punishment that stretches from Thursday through the 2014 season for violations of its drug agreement and labour contract. Hours after the suspension was handed out, he made his season debut and got booed every time his name was announced.
It was the same way on Tuesday. The only time he heard cheers was when Sale hit him with a pitch near the belt in the third inning.
NOTES: The White Sox held LF Dayan Viciedo out of the lineup after he jammed his left thumb on Monday. Manager Robin Ventura said he was available as a pinch hitter and expected Viciedo back in the lineup on Wednesday. ... Yankees closer Mariano Rivera insisted he's still retiring at the end of the season and will not reconsider. ... Manager Joe Girardi said C Francisco Cervelli, who was suspended 50 games on Monday, had surgery to remove hardware from his right hand. ... RHP David Phelps will likely be out a few more weeks after sustaining a different strain in his pitching forearm than the one that landed him on the disabled list last month. And RHP Michael Pineda will be shut down for a week to 10 days after he left his start with Triple-A Scranton/Wilkes-Barre on Friday because of shoulder stiffness.