Dunn, 29, led off the seventh inning and smoked Tommy Hanson's 2-2 pitch into the second deck in right field to cut the Braves' lead to 3-1. The ball was caught by U.S. Army colonel William Sanders.
"It was just over the plate," said Hanson about Dunn's home run. "It was supposed to be a fastball inside, but I left it over the plate, and he let me know. That's really the only one that hurt me."
It was Dunn's 22nd home run of the season, and he also received his first curtain call of the year. The Nationals then had a video montage of all the home runs Dunn hit this year.
Dunn becomes the 123rd member of the 300-home run club and just the 13th player to reach the 300-homer plateau before the age of 30.
Dunn said the long ball was special because the Nationals were able to win the game.
"It really wasn't that significant at the time," said Dunn. "The reason I said it because it was a solo home run. We were down by two. What made it special [later on] was the way we won the game. That was awesome in the eighth inning.
"The way the crowd got into it. I don't know how many people were here. But from the seventh inning on, it was very loud and energetic. They made it great. It was awesome."
Hitting a home run wasn't the only thing Dunn did in the game. He drove in the game-winning run, a single to right field against left-hander Eric O'Flaherty in the eighth.
"That 300th home run would have been hard to talk about because it would have been a useless home run if we didn't win that game," Dunn said.
After the game, Sanders gave Dunn his special ball back to him. Sanders didn't want anything in return, but Dunn gave him an autographed jersey, a couple of balls and some tickets for future Nationals games.
"The guy was awesome, but some people would think that ball is worth more," Dunn said. "He is such a class person. I couldn't hit it to a better guy."
How many more home runs can Dunn hit? Can he reach 500 home runs?
"That's an incredible number," Dunn said. "There are a lot of things that have to go right. You have to stay healthy. You have to be very productive for a long time. I'm going to sit here and say I don't know."
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.