Michael Morse hit a pair of home runs as the 2, to begin a four-game series.
John Lannan (9-11) allowed one run on five hits and two walks though 5 1/3 innings to earn his first win since August 2.
Hiroki Kuroda (11-15) tossed six innings, yielding five runs on eight hits while striking out nine. His career-high four-game winning streak was broken.
Matt Kemp and Justin Sellers each had run-scoring doubles as Los Angeles dropped its second straight contest after a six-game win streak.
The Dodgers took the early lead on back-to-back doubles by Jamey Carroll and Kemp in the top of the first.
But Washington answered in the home half of the inning with three home runs. Desmond led off the frame with a shot to left. Three batters later, Morse lifted a two-run homer and Werth followed with a home run into the left-field bleachers to put the Nationals ahead, 4-1.
"I settled down after they scored," Lannan said. "It's always a little bit of a comfort when you can go out there and just get ahead when you know you have a lead."
Morse increased the Nats lead with his second home run of the game in the sixth, a leadoff blast into the bullpen in left-center field.
Rick Ankiel's run-scoring double in the seventh off of Josh Lindblom and Wilson Ramos' RBI single in the eighth against Ramon Troncoso made it a 7-1 game.
A.J. Ellis and Sellers hit consecutive doubles in the ninth inning to bring Ellis across the plate and account for the final score.
The Dodgers best chance to get back in the game came in the fourth inning when they put runners on first and second with no outs on a Juan Rivera walk and a base hit to left by Aaron Miles. Russ Mitchell followed with a bouncer to third. Ryan Zimmerman grabbed the ball near the bag, stepped on it for the force, fired to second for the force there and the play almost ended in a 5-4-3 triple play, but Danny Espinosa's toss to first was wide. Mitchell took second on the error, but did not advance any further as Tony Gwynn Jr. flied out to left to end the inning.
"We never really got anything going," Dodgers manager Don Mattingly said.
Ramos extended his hit streak to nine games...Kuroda fell to 7-6 in 13 road starts this season...Washington won despite hitting just 1-for-5 with runners in scoring position and leaving six men on base...Los Angeles went 2-for-8 with runners in scoring position and stranded eight.