Kershaw (6-4) ended a personal three-start winless streak, holding the Mets to three runs (one earned) on five hits while striking out nine to offset three walks.
The Dodgers used three Mets errors to rally from a 3-1 deficit, including first baseman Justin Turner's fielding error in the fifth and catcher Mike Nickeas' two-run miscue in the seventh.
James Loney drove in two runs while Dee Gordon added an RBI to go with three stolen bases as the Dodgers won for the first time in a week and avoided a four-game series sweep.
Mets starter Dillon Gee (5-7) surrendered four runs (two earned) on five hits over six full innings.
Scott Hairston supplied New York's only RBI.