Kershaw (20-3) pitched five shaky innings in his shortest start in 3 1/2 months, but the NL West-leading Dodgers roughed up Edwin Jackson on their way to a 13-hit attack that included four homers. Matt Kemp hit a three-run shot in Los Angeles' six-run first, and Yasiel Puig added another three-run homer in the sixth.
The Dodgers improved baseball's best road record to 48-31 and will clinch a postseason berth if Milwaukee loses in Pittsburgh on Friday night. They began the day with a 2 1/2-game lead over San Francisco in the division.
Jackson (6-15) recorded just two outs in his first appearance since he was placed on the disabled list last month with a right lat strain. He was charged with four hits and five runs in his fourth consecutive loss.
