Dempster (11-8) walked two and struck out six in recording his 10th career complete game and third career shutout. It was his first shutout in more than eight seasons.
Jeff Baker, Micah Hoffpauir and Derrek Lee each had two RBI for Chicago, which has won four of its last five games but will be officially eliminated from the playoffs if Colorado beats Milwaukee Tuesday.
Kevin Hart (4-9), who the Cubs traded to Pittsburgh in July, took the loss after giving up six runs on six hits in four innings.
Copyright 2009 by United Press International.