Floyd (2-2) gave up just two hits and a walk with six strikeouts for the Braves, who were coming off a three-game sweep at the hands of the Phillies. Freddie Freeman went 3-for-5 with two runs scored.
The game stayed scoreless until the fourth inning when the Braves went on top. Freeman, Evan Gattis and Jason Heyward all singled with one out to load the bases for Johnson, who punched a single up the middle and just past the glove of Danny Espinosa to chase home two runs. Ryan Doumit flied out and Andrelton Simmons struck out to end the frame.
Washington left a man on second in the third in the sixth, while Werth doubled to start the seventh. He was left there though, as Adam LaRoche, Ryan Zimmerman and Ian Desmond all grounded out to end the frame.
In the eighth, Freeman doubled to start the frame and Gattis followed with a single. Two batters later, Johnson singled to left for a 3-0 advantage.
Jordan Walden pitched a 1-2-3 eighth inning, while Craig Kimbrel worked around a one-out walk in the ninth for his 21st save of the season.