Ethier's blast in the sixth gave the Dodgers an 8-5 lead and National League West-leading Los Angeles went on to take the opener of a three-game series.
Kershaw (14-8) earned the victory despite coughing up five runs on 11 hits in a five-inning performance.
Kenley Jansen notched his 25th save as the Dodgers opened up a 12 1/2-game lead over second-place Arizona.
Dodgers star rookie outfielder Yasiel Puig left the game in sixth inning with strained knee.
Jeff Manship (0-5) took the loss for the Rockies.
Wilin Rosario homered and Charlie Blackmon went 3-for-5 with an RBI in Colorado's defeat.