Freddie Freeman doubled three times and scored twice, helping the NL West leaders win for the 16th time in 21 games.
Austin Barnes homered and drove in three runs.Kershaw gave up five hits, struck out two and walked one.
The three-time Cy Young Award combined with two relievers on the Dodgers' third shutout of the season. Barnes hit a solo drive in the fourth against Drew Smyly and added a two-run single in the eighth.
Justin Turner drove in two with a double in the fifth, making it 4-0.