The Dodgers' third straight win lowered their magic number to 12 to clinch the National League West.
Kershaw struggled with command early, walking D.J. LeMahieu after getting ahead in the count 0-2 in the first inning, then walking Jon Gray in the third, the first walk Kershaw issued to a pitcher all season.
That first walk proved to be crucial since it was followed by a double to the right center field gap by Nolan Arenado, followed by a Carlos Gonzalez ground out to score LeMahieu.
But that was pretty much it for Kershaw, who allowed just three hits on the night, and retired 14 of his final 16 batters faced. Kershaw struck out five, matching a season low for him, giving him 264 strikeouts on the season with likely four starts remaining.
Monday night was also the seventh straight start for Kershaw of at least seven innings allowing zero or one earned run, the longest streak by a Dodgers pitcher since Fernando Valenzuela's first seven major league starts in 1981.
But Kershaw mania extends farther back than just his last seven starts. In his last 13 starts, dating back to July 3, Kershaw is 9-0 with a 0.98 ERA, with 12 runs (11 earned) and 13 walks allowed, to go with 124 strikeouts in 101 innings.
Gray was matching Kershaw for a while, and set a new career high with eight strikeouts in his eighth career start. He allowed a run in the second inning, then had two outs in the fifth before he hit a wall. He walked Chase Utley, then Adrian Gonzalez singled him to third base. Justin Turner followed with a double to left, giving the Dodgers their first lead and ending Gray's night.
Yasmani Grandal drove in the first run of the game for the Dodgers with a sacrifice fly to the warning track in left center field, then singled in his first two at-bats, the first of which was clocked at 112 mph off the bat. That snapped an 0-for-36 skid for the catcher.
Corey Seager in his home Dodgers debut doubled, singled and was hit by a pitch in his four plate appearances. He has reached base in all 10 of his major league starts, and through his first 11 games owns a .543 on-base percentage.
Seager's eighth-inning single was followed by a two-run shot by Scott Schebler, giving the Dodgers some insurance runs for the ninth.
After a 33-pitch performance on Sunday rendered Kenley Jansen unavailable for Monday, Chris Hatcher pitched the ninth inning for his third save of the season, and his first since May 2. Since returning from the disabled list on Aug. 15, Hatcher has a 1.35 ERA in 13 games and a 30.8-percent strikeout rate.
WP - Clayton Kershaw (14-6): 7 IP, 3 hits, 1 run, 2 walks, 5 strikeouts
LP - Jon Gray (0-1): 4⅔ IP, 6 hits, 2 runs, 2 walks, 8 strikeouts
Sv - Chris Hatcher (3): 1 IP, 1 hit