Hudson (2-0) logged a second straight start in which he has held his opponents to just a single run over at least 6 2/3 frames. The right-hander yielded four hits, didn't issue a walk and struck out three.
Eric O'Flaherty tossed a scoreless eighth and Craig Kimbrel notched his sixth save with a 1-2-3 ninth as Atlanta reeled off an eighth straight win while clinching its three-game set at Nationals Park.
Evan Gattis smacked a two-run homer and Jason Hayward added an RBI for the Braves, who improved to 10-1 to start the season.
Nats starter Stephen Strasburg (1-2) absorbed the loss despite not allowing an earned run. The right-hander fanned seven while surrendering five hits and one walk over six innings.
Danny Espinoza socked a solo homer for Washington.