Last year's National League Cy Young Award winner pitched a complete game three-hitter, as the Dodgers defeated the Brewers, 3-1 at Miller Park in the opener of a three-game series.
Kershaw's ERA this season is now a paltry 1.35.
Yovani Gallardo (3-4) took the loss for Milwaukee. He allowed an RBI triple to Andre Ethier in the second inning to make it 1-0. Ethier then homered in the fourth to give Los Angeles a 2-1 lead. Matt Kemp then homered off Gallardo in the sixth to complete the scoring.
The Brewers and Dodgers will continue their series on Tuesday night at Miller Park. Former Brewer Zack Greinke will take the mound for Los Angeles in the contest.
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