Gorzelanny (2-4) gave up three hits and struck out five before leaving the game with an injury to his left ring finger. X-rays were negative.
Chicago was nursing a 2-1 lead going into the ninth, but got some insurance when Xavier Nady produced a two-run single after the Cubs had loaded the bases on two walks and a hit batter.
Carlos Marmol put two runners on with one out in the ninth, and then struck out Ross Gload and Shane Victorino to collect his seventh save.
Philadelphia has lost two in a row after winning four straight.