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Kershaw allowed two runs in the first and was pulled with no outs in the second after giving up a homer to Corbin Carroll to start the inning.
Kershaw, 36, has made seven starts since making his season debut in late July. He is 2-2 with a 4.50 ERA.
Right-handed reliever Joe Kelly, who threw 1⅔ innings in relief of Kershaw on Friday night, also was placed on the injured list Saturday with right shoulder inflammation.
In corresponding moves, the Dodgers called up right-handers Brent Honeywell and Ben Casparius from Triple-A Oklahoma City.
