Scott Diamond (1-2) allowed three runs on three hits and three walks while fanning five through six innings to earn his first career victory.
Joe Nathan allowed two runs in the ninth, but left the game-tying run on the bases to earn his 12th save of the year.
Jake Peavy (6-7) allowed six runs -- all in the first inning -- on eight hits in five innings. He did not issue a walk and struck out four.
Chicago remains six games back of the Detroit Tigers for first place in the AL Central. The two clubs start a three-game set in Detroit on Friday.