Peacock (12-2) allowed two runs on one hit with six strikeouts. The right-hander continues to throw well, allowing two runs or fewer in each of his last five starts.
After Yoan Moncada put the White Sox up 2-1 in the top of the fourth with a two-run homer, Gurriel answered with his two-run hit in the bottom half of the inning.
Jose Altuve upped Houston's lead to 4-2 with an RBI single in the seventh, but Yolmer Sanchez cut the lead to one with an RBI double in the eighth.
Joe Musgrove struck out Moncada with the tying run on second to end the eighth and struck out Omar Narvaez with the tying run on second to end the game for his second save.
James Shields (4-7) allowed three runs on six hits with four walks and five strikeouts in 5 2/3 innings. Shields has given up at least three runs in five of his last six starts.
