Thomas hit solo homers in the fourth and eighth innings, giving him 433 for his career. He passed Cal Ripken Jr. for 31st on the all-time list.
Lee, who went 3-for-5, moved within one game of the longest streak in team history, a mark shared by Lance Johnson and Albert Belle.
The White Sox, who defeated the Braves for the first time in five meetings, scored four runs in the second and one in each of the next six innings.
Atlanta erased a 6-2 deficit with four runs in the fifth, tying it on a two-run homer by Chipper Jones.
Chicago starter Esteban Loaiza (7-3) got the win.