Maholm gave up eight hits but only one run while leveling his record at 6-6 with his second consecutive victory. The two straight wins have come after he had gone seven weeks without one.
Chicago had a 2-1 lead when Maholm left the game, one of the scores coming on Bryan LaHair's 14th homer in the fourth.
After Maholm exited the contest, Jeff Baker and Anthony Rizzo added solo shots in the seventh and eighth innings.
Randall Delgado (4-9) took the loss, giving up three runs on seven hits in six innings.