Kemp finished 3-for-4 while Crawford and Mark Ellis each provided three hits for Los Angeles, which stayed hot with a three-game series sweep.
Kershaw (9-6) turned in a dominating performance, limiting the Nationals to two hits -- a pair of Jayson Werth solo homers. The Dodgers ace didn't issue a walk, struck out nine and drove in a run on his way to the win.
Los Angeles, which came into the contest trailing National League West-leading Arizona by one-half game, reeled off its ninth win in 11 contests.
Washington starter Jordan Zimmermann (12-5) was torched for seven runs on eight hits over just two full frames.