Kershaw (11-6) won his fourth straight start and the Dodgers' winning streak reached four as well. Los Angeles has defeated Pittsburgh in each of their last nine meetings.
The Los Angeles pitcher singled in the fourth and scored on Matt Kemp's two-run double that gave the Dodgers a 5-1 lead. Kemp had three RBI overall.
Los Angeles broke things open with a four-run seventh. Luis Cruz doubled home a run during the inning and later scored on the sacrifice fly by Kershaw. It was the eighth RBI of Kershaw's five-year career.
Wandy Rodriguez (7-12) gave up five runs on 10 hits in 5 2/3 to take the loss. He has an 0-3 record with Pittsburgh since coming over from Houston in a four-player deal July 24.