The Dodgers won for the fourth time in five games after suffering through an eight-game losing streak.
Adrian Gonzalez and starting pitcher Zach Greinke both singled in a run to give Los Angeles a 2-0 lead through two innings and Carl Crawford added an insurance tally with a sacrifice fly in the eighth.
Greinke (2-0), making his first start since April 11 after suffering a broken collarbone, went 5 1/3 innings to get the win. He allowed the lone Washington run on five hits with four strikeouts.
Washington starter Ross Detwiler (2-4) suffered an apparent injury while covering first base in the third inning. He finished the third, but did not come out for the fourth and wound up taking the loss.