Joaquin Arias added a two-run single in the first inning and Julio Borbon had an RBI base hit. The game-winning run, however, was not scored until the seventh, when David Murphy doubled in Michael Young with two away.
That gave Texas a 6-3 cushion going into the ninth and the extra run was needed when closer Neftali Feliz made things interesting.
With two out and a runner on second, Feliz gave up a run-scoring double to A.J. Pierzynski, threw a wild pitch and surrendered an RBI single to Alexei Ramirez. Juan Pierre then grounded out to end the game, giving Feliz his third save.
Jake Peavy (0-2) took the loss, allowing six runs on six hits in 6 1/3. The White Sox have lost six straight on the road.