Chicago captured both contests in the two-game series, extended its winning streak to three and has won nine of its last 12.
Four players drove in two runs each for the White Sox, who had 10 hits and got a solid seven-inning effort from Gavin Floyd.
Paul Konerko had a two-run double in the first and Chicago broke the game open in the second on a two-RBI double from Ramirez and a two-run single by Adam Dunn.
Carlos Quentin added a two-run homer in the fifth.
Floyd (5-3) gave up a run on five hits. Fausto Carmona (3-4) was charged with the loss, surrendering eight runs on seven hits in five innings.