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 winner bounced back from a tough-luck loss to Detroit in which he surpassed Hall of Famer Don Sutton as the Dodgers' career strikeout leader.
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 and the Dodgers continued to roll along coming off a two-game sweep of San Francisco in which they outscored their rivals by a combined 12-2.
Smyly lasted 4 1/3 innings in his return from the bereavement list. The left-hander allowed two earned runs and six hits.