Hudson (14-8) allowed one run on five hits to record the win. He walked two and struck out five.
Alex Gonzalez had a pair of RBI for the Braves, who have won nine of 12 and lead the NL Wild Card race by a comfortable 8 1/2 games.
A night after setting the major league rookie saves record, Craig Kimbrel struck out the side in the ninth to record his 42nd rescue of the season.
Chien-Ming Wang (2-3) lasted 5 2/3 innings, surrendering four runs on seven hits to suffer the loss.
Jayson Werth hit a home run for the Nationals, who have dropped eight of their last nine games.