Dempster (10-8), who took a no-hitter into the fifth, gave up just four hits and walking one for the Cubs, who have won six of their last seven games.
Aramis Ramirez had a pair of hits for Chicago.
Jeff Suppan (6-10) gave up one run on three hits with four walks in seven innings to take the loss. Suppan has won just once in his last 13 starts.
Copyright 2009 by United Press International.