The win gives Los Angeles their ninth division title in the last 10 seasons.
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Kershaw only gave up two hits and struck out five before he was taken out after seven innings in the Dodgers 4-0 win at Chase Field.
Freddie Freeman, Joey Gallo and Max Muncy each hit homers on the night. Gallo hit a 2-run bomb to center field.
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Los Angeles is now 98-43 on the season, the best record in the majors. L.A. on Monday became the first club this season to clinch a postseason berth.
The Dodgers lead second-place San Diego by a whopping 20 1/2 games in the division.
Manager Dave Roberts' team will have plenty of time to get set for its 10th straight year in the postseason. The Dodgers' first playoff game is almost a month away, on Oct. 11.
The only season the Dodgers didn't clinch the division in their recent run was last year - they won 106 times but still finished one game behind San Francisco. Los Angeles then beat the Giants in the NL Division Series before falling to eventual champion Atlanta in the NLCS.
The Associated Press contributed to this report.