Teixeira's homer to right came during a five-run rally in the seventh inning. Damon homered in the third.
The Yankees are 31-11 since the all-star break.
Alfredo Aceves (9-1) recorded the win, allowing two hits in three innings.
Jermaine Dye belted a solo home run and Scott Podsednik and Gordon Beckham each had an RBI for the White Sox, who have dropped seven of eight.
Freddy Garcia (0-2) was the losing pitcher, giving up three runs and four hits in six innings.
Copyright 2009 by United Press International.