Hudson held Washington to seven hits in a complete game, the first by an Atlanta pitcher this season, and the Braves topped the Nationals 3-0 on Sunday to remain within striking distance of the wild-card leaders.
Hudson (16-8) broke a three-game losing streak and needed only 100 pitches for his 10th career shutout and 21st complete game. Hudson is 4-0 and has allowed just two runs in 30 innings against the Nationals this season.
"I have never been a complete game guy. I don't really care about shutouts," Hudson said. "The most important thing is to get a win for the ballclub."
The Braves closed within 7½ games of front-running New York in the NL East, after the Mets lost 10-6 to Philadelphia. Atlanta began the day 5½ games behind the San Diego Padres in the NL wild-card race.
Atlanta's bullpen had been taxed in the first two games of the series. The Braves won a 13-inning game on Friday, and Saturday starter Lance Cormier was knocked out in the third inning.
"Complete games are always rewarding, don't get me wrong," Hudson said. "It is great to see the bullpen guys come in (after the game) and see a big smile on their face and know they had the day off. It was nice to go out there and do it."
The right-hander allowed two first-inning singles and scattered five more hits the rest of the way. D'Angelo Jimenez led off the sixth with a double, advanced to third on an infield out and was stranded there. Hudson walked one, struck out six and added a single and double.
"We just don't match up very well against him," Washington manager Manny Acta said.
Ryan Zimmerman had one of the four hits, but he's only 2-for-13 against Hudson this year.
"He's dominating a lot of teams," Zimmerman said. "He's one of the best pitchers in the game -- and they just don't say that about people for nothing."
Atlanta got the only runs it needed in the third on Mark Teixeira's two-run, bases-loaded single. Hudson led off with an infield single, and one out later, Edgar Renteria and Chipper Jones drew walks. Teixeira followed with a base hit off Shawn Hill just past first baseman Robert Fick's glove.
"It was the best I have seen him pitch since I have been here," Teixeira said of Hudson, who made the lead stand. "We should have scored more runs than we did, but three was all he needed."
Added manager Bobby Cox: "He has pitched good against this team. He had the sinker and the breaking stuff working. He had good stuff today."
Hill (4-4), who missed three months with a sore right elbow, lost for the first time since May 1. In his previous eight starts, he had two wins and six no-decisions.
"It was a big win," Teixeira added. "It was another win we needed to get. We still have a chance, so we are going to keep trying. We know we have our work cut out for us."