Instead, they'll focus on winning their ninth straight home game over the Yankees on Saturday.
Adam Dunn's two-run homer in the ninth inning gave Chicago (25-25) its fourth victory in five games, 6-5 on Friday. The White Sox's eight-game winning streak against New York (24-23) on the South Side is the club's longest such active run against any opponent.
It's also the Yankees' longest current road slide against a single team. A loser in four of five, New York's last four defeats at U.S. Cellular have come by one run.
"I'm not sure it means that much," said Dunn, who has homered for three of the seven hits in his last 26 at-bats and has nine RBIs during that span.
"You've got to play really well at home to do anything. We just play these guys really tough."
Alexei Ramirez hit a two-run homer for Chicago, which rallied after Brian McCann hit a three-run shot in the first inning.
Ramirez is batting .469 with two home runs and six RBIs during the home win streak versus New York.
Chicago's John Danks (3-4, 5.64 ERA), who hasn't faced the Yankees since 2011, posted a 4.38 ERA while winning his first two home starts against them but has a 10.45 ERA in losing the last two versus New York there.
Danks also looks to avoid losing his third straight start overall after he gave up eight runs and 10 hits, including three homers, in 4 2-3 innings of an 8-2 defeat at Houston on Sunday. The left-hander has allowed seven home runs in the last four starts after yielding one in his first five.
"Everyone's going to have bumps in the road like this,'' manager Robin Ventura said. ''But you need him to keep the ball down, especially the way he pitches."
Mark Teixeira and Jacoby Ellsbury are a combined 13 for 23 versus Danks, but together have gone 1 for 14 with six strikeouts in the first two games of this series.
Ellsbury is 4 for 43 in his last 12 contests.
Vidal Nuno (1-1, 5.82) makes his first appearance against the White Sox and seventh straight since moving from the bullpen. The left-hander is 1-1 with a 4.55 ERA in his six starts, but has yielded one run and seven hits over 11 1-3 innings while going 1-0 in two on the road.
His last two overall came at home, most recently Sunday when he gave up three runs in six innings while not factoring in the decision of a 5-3 loss to Pittsburgh.
New York's Derek Jeter, who singled twice Friday, tied White Sox great Luis Aparicio for second in games played at shortstop with 2,583.
''I guess it is ironic that we're here,'' Jeter said. ''It's hard to believe when you think about the history of the game that there is only one guy that's played more games. It's something I'm proud of."
Jeter is batting .353 with two doubles in 17 at-bats versus Danks.