Anderson, pinch-hitting for Juan Rivera, lofted a fly ball to right field, scoring Gary Matthews Jr. from third base with one out in the top of the eighth. It was his 75th RBI this season.
Rivera also knocked in a run and Torii Hunter had two hits and one RBI for the AL West-leading Angels, who averted a three-game sweep.
Winning pitcher Joe Saunders (15-7) gave up two earned runs and just four hits in 7 1/3 innings.
Closer Francisco Rodriguez registered his 55th save, moving to within two of the White Sox's Bobby Thigpen's all-time single-season record.
The victory, coupled with the Texas Rangers' 7-2 loss to Boston Sunday, reduced the Angels' magic number to three for cliching the AL West title.
Chicago scored on solo homers by Paul Konerko in the fourth and Toby Hall in the fifth. Konerko had two of the five hits for the White Sox, who remained 2 1/2 games ahead of Minnesota atop the AL Central Division.
The losing pitcher was Horacio Ramirez (1-4).