Danks (14-11), who gave up seven hits, fanned five batters and walked two to pick up his first win since September 4 for Chicago, which has won three in a row since an eight-game skid.
Ramon Castro hit a solo homer for the White Sox, who got two RBI from Alexei Ramirez. Alex Rios, Juan Pierre, and Manny Ramirez each knocked in a run.
Chicago has won six in a row versus Los Angeles for the first time since April 7- June 10, 1992.
Howie Kendrick and Torii Hunter had an RBI apiece for Los Angeles, which has lost three in a row.
Scott Kazmir (9-15) lasted just three-plus innings in the start, allowing five runs on five hits. The left-hander is 1-6 over his last nine starts.