Teixeira went deep as a lefty and righty in the same game for the 12th time in his career, surpassing Eddie Murray and Chili Davis for most all-time.
The feat somewhat overshadowed Hughes (2-3), who did not allow a runner into scoring position in the first shutout of his career. The 25-year-old right- hander gave up just three hits with no walks and four strikeouts in six innings.
"I wanted to pitch well, and I knew I could do better than what I had been showing," Hughes said.
New York has won eight of 10 overall, but still sits a game back of the Boston Red Sox with a three-game series between the two rivals slated for this weekend at Fenway Park.
"My job is to get the best things out of those guys; I don't care how," White Sox manager Ozzie Guillen said.
Tonight, the Yanks turn to righty A.J. Burnett, who is 0-3 in his last five starts. Burnett fell to 8-9 on the year on Friday against Baltimore, which reached him four runs and five hits in eight innings. He also struck out a season-high 10 batters in the loss, but saw his ERA jump to 4.23.
"I gave all I could out there," Burnett said. "Where I'm at now, I feel fine. I can't wait to pitch the next game."
Burnett lost to the White Sox earlier in the year, despite giving up just one run in eight innings and is 2-5 lifetime against them with a 4.84 ERA in eight starts.
Chicago will counter with righty Gavin Floyd, who has won his last three starts after going 0-4 in his previous six.