Dempster (7-7) threw 101 pitches with a walk and five strikeouts.
Closer Carlos Marmol earned his fifth save with a scoreless ninth.
Jake Fox had four hits -- one a solo homer -- and two RBI. Kosuke Fukudome had one RBI, while Ryan Theriot added two hits for the Cubs, who have won just four of their last 14 games.
Los Angeles scored on Tony Abreu's second-inning single. Andre Ethier and Juan Pierre had one hit apiece for the Dodgers, who had beaten the Cubs four straight times.
Losing pitcher Chad Billingsley (12-7) gave up three runs and nine hits in six innings with a walk and five strikeouts.
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