Hudson (16-8) broke a personal three-game losing streak. He yielded seven hits while walking one and striking out six, for his first shutout of the season.
The Braves entered the day 8 1/2 games behind the first-place New York Mets in the NL East and 5 1/2 games behind the San Diego Padres in the NL wild-card race.
D'Angelo Jimenez doubled and singled for the Nationals, who have lost four of five.
Washington starter Shawn Hill (4-4) went five innings, giving up three runs on five hits with four walks and two strikeouts.