Wood (8-10) allowed one unearned run on five hits and two walks while striking out six over six strong innings to snap a personal three-game losing streak and hand the high-octane Dodgers their third loss in four games.
Kevin Gregg earned his 27th save despite putting the tying run on base in the bottom of the ninth.
Kershaw (13-8) lasted 5 2/3 innings. The Los Angeles ace surrendered two runs – one earned – on seven hits with nine strikeouts.
Andre Ethier and Juan Uribe notched an RBI apiece for the Dodgers.