Kershaw (12-7) scattered just three hits, issued a single walk and struck out eight on his way to a sixth straight start of allowing two or fewer earned runs.
The 2011 Cy Young Award winner lowered his major league-best ERA to 1.80 with the performance as the National League West-leading Dodgers reeled off their 10th straight win.
They improved to 42-8 over their last 50 games, tying the MLB record for best mark ever over a 50-game span, joining the 1941 New York Yankees and the 1942 St. Louis Cardinals.
Juan Uribe led Los Angeles at the plate, going 3-for-3 with a three-run homer in the ninth inning.
Kyle Kendrick (10-10) took the loss despite allowing just one earned run on seven hits in a six-inning effort.