Winning pitcher Shawn Chacon got his second win as a Yankee. Chacon had lost eight consecutive decisions dating back to before his trade from Colorado earlier this season.
He hurled eight scoreless innings, scattering four hits, walking three and fanning five.
The Yankees have won the first two games of the weekend series and seven of their last nine overall.
In relief, Felix Hernandez retired the side in order in the ninth to preserve New York's eighth shutout of the season.
The American League Central Division-leading White Sox have lost seven straight, their longest skid of the season.
Tadahito Iguchi had two hits but outfielder Carl Everett had his seven-game hitting streak broken for Chicago.
The loser, former Yankee Orlando Hernandez, fell to 8-6.