Uribe hit a run-scoring double and Hall added an RBI single in the top of the second inning. Hall was one of four players with two hits for the White Sox, who have won four of their last five games.
Winner John Danks (10-5) allowed an earned run and six hits in six innings with five walks and five strikeouts.
Closer Bob Jenks recorded his 25th save by retiring the side in the bottom of the ninth.
Oakland's run scored on Emil Brown's third-inning single. He had two of the six hits in the Athletics' 24th loss in their last 28 games overall.
Losing pitcher Greg Smith (5-12) gave up two earned runs and eight hits in five innings.