At 13 games over .500, the Yankees have matched their high-water mark this season.
"We've got to collect wins. They have a great cushion over there and we don't," said Alex Rodriguez, who hit a two-run double.
Hernandez threw behind Rodriguez on the first pitch of the second inning and both benches were warned by plate umpire Larry Vanover.
"I'm not a machine. I never throw intentional," said Hernandez, who had a couple of conversations with the umpire.
A-Rod declined to comment on the pitch.
"I didn't think it was an accident. He has too good of command. There was a purpose for it and I'm not sure what it was," Yankees manager Joe Torre said. "But I thought Larry Vanover did the right thing."
That was just the beginning for El Duque. He committed his first two errors in 109 games and was also called for a balk. He gave up six hits and five runs -- four earned -- in six-plus innings.
"It's been a long time since I've had an error and then committing two in one day is frustrating," Hernandez said through a translator.
Hernandez (8-6), who went 61-40 in the regular season and 9-3 in the postseason during two stints with the Yankees from 1998-04, lost to his former team for the second time this month. He's dropped three straight starts and five of six decisions.
Chicago has scored two runs in the last 36 innings, and the AL Central leaders have lost 15 of 21 home games.
"It's embarrassing to me. I don't know if it is embarrassing to the players," White Sox manager Ozzie Guillen said. "It gets to the point where you are sick to your stomach. We are having terrible at-bats. ... We just stink at the plate."
Felix Rodriguez finished the four-hitter for the Yankees, who have allowed only seven runs in five games against the White Sox this season.
Chacon said he watched Mike Mussina shut down the White Sox on Friday night in a 3-1 Yankees victory.
"It's great following him," Chacon said. "He told me to watch the hitters to see if they change their approach. I mixed it up and kept them off balance."
Derek Jeter and Bernie Williams singled in the fourth for the first two hits off Hernandez. He then gloved Gary Sheffield's comebacker and tried to start a double play, but his throw sailed untouched into center field because shortstop Juan Uribe and second baseman Tadahito Iguchi got confused on who was covering and Iguchi arrived late. Still, Hernandez was charged with his first error since Aug. 17, 1999.
"I just threw the ball to second. I never knew who was going to cover. I just threw it across the bag," Hernandez said.
Jeter scored and Williams went to third before Rodriguez hit a two-run double past the bag at third. Hernandez was then called for a balk, but Rodriguez, who moved to third on the call, was picked off by catcher A.J. Pierzynski.
Williams' bases-loaded sacrifice fly put New York up 4-0 in the fifth.
Chicago squandered a big chance in the third after Geoff Blum singled leading off and Uribe walked after a 13-pitch at-bat. With the Yankees expecting a bunt, Blum broke for third and Timo Perez swung away, popping to Jeter at shortstop in what turned into an easy double play for the Yankees.
Hernandez was charged for his second error in the sixth when first base umpire Randy Marsh ruled he missed the bag after taking a throw from first baseman Blum on Matsui's grounder. Hernandez and Guillen argued, and replays showed Hernandez's toe appeared to clip the bag as he crossed it.
- Rodriguez was 1-for-13 before his fourth-inning double.
- New York's Jason Giambi was 0-for-2, extending his hitless streak to a career-worst 20 at-bats. He left with a bruised right calf in the sixth.
- The White Sox played a second straight game without their leading run producer, Paul Konerko, who strained his back in batting practice Friday. He leads the team in homers and RBI.