Chicago Cubs right-hander Ryan Dempster did not allow a run in six innings of a 4-1 win over the Arizona Diamondbacks Saturday, extending his consecutive scoreless streak to 33. Dempster's streak matched Ken Holtzman in 1969 for the team record. Dempster has not surrendered a run since May 30, a span of five starts. It was also his fifth straight win. The Cubs are 11-4 in their last 15 games. Dempster scattered four hits and walked three. He was taken out of the game after throwing 89 pitches as manager Dale Sveum was limiting Dempster to between 85 and 95 pitches because he recently had a lat injury. Right after Dempster departed with Chicago up 4-0, reliever James Russell gave up a solo home run to Chris Young in the seventh inning but the Cubs held on the rest of the way.