Ryan Braun managed a pair of singles and Yuniesky Betancourt also singled for the only hits off Kershaw (5-2). The lefty struck out five and walked one.
Andre Ethier homered and tripled for the last-place Dodgers before being ejected by plate umpire Dan Bellino for arguing a called third strike in the eighth inning.
The victory was a respite for Dodgers manager Don Mattingly. He addressed speculation before the game on whether he would be fired this week, insisting he didn't feel as if he was about to be replaced.
Yovani Gallardo (3-4) gave up three runs, including two homers, in six innings. The right-hander lost his third consecutive start and the reeling Brewers have dropped 15 of 18 games.
With the Dodgers' bullpen giving up 12 runs while Los Angeles was swept in a three-game weekend series at Atlanta, Mattingly took no chances. He sent Kershaw out for the ninth, and the ace needed only 10 pitches to retire the Brewers in order.
Dodgers general manager Ned Colletti said before the game he thought Kemp's lack of power this season was due to the slugger's offseason surgery on his left shoulder.
The star center fielder hit his second homer of the season, connecting for the first time in a span of 87 at-bats. Kemp's solo homer came in the sixth.
Colletti said his team, second-to-last in the majors in scoring at 3.4 runs per game, needed to hit better in the clutch. The Dodgers went 0 for 6 with runners in scoring position against the Brewers.
Kershaw beat the Brewers for the second time in five starts. He has given up only three earned runs in 39 2-3 innings for an 0.68 ERA in that span.
Kemp, who hit 116 homers the past four seasons, walked to lead off the second and scored easily on Ethier's triple for a 1-0 lead.
The Brewers tied it in the third. Rickie Weeks walked and later scored on a groundout to second by Norichika Aoki.
Ethier's solo homer, his fourth, put the Dodgers ahead in the fourth.
NOTES: Dodgers LHP Ted Lilly was reinstated off the 15-day DL. RHP Matt Magill was optioned to Triple-A Albuquerque. Lilly will spend a couple of days in the bullpen and is expected to start Saturday against St. Louis. ... Dodgers INF Jerry Hairston has tendinitis in his left knee.
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