Dempster (1-3) gained his initial victory of the season after 10 starts for the last-place Cubs, tossing a perfect game into the sixth inning. The right-hander ended up allowing three hits without a walk and striking out three.
Shawn Camp and Jairo Asencio completed the shutout with one scoreless frame each as Chicago claimed the opener of a three-game series at Miller Park.
Milwaukee starter Yovani Gallardo (4-5) struck out 10 but yielded five runs on six hits in six full frames.
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