For the Nationals, it was a relief just to get a win of any kind.
"I don't remember the last time we had a lead," manager Jim Riggleman said.
Dunn supplied that early, connecting with a 1-1 changeup that Jair Jurrjens left in the middle of the plate. The two-run shot in the second inning was the 35th of the season for Dunn and the ball just kept carrying and carrying.
Sammy Sosa is credited with the longest homer at Turner Field, a 471-foot smash for the Cubs in 2001. Dunn's blast appeared to rival it, although the distance was listed as 455 feet.
"I don't know who is measuring these balls," Nationals shortstop Ian Desmond said.
Dunn, though, wasn't quibbling. He hit a homer in Colorado that might still be going if it hadn't landed in the third deck at Coors Field.
"I know this is a very a big ballpark and you have to hit it good to get it out of here," Dunn said of the homer off Jurrjens. "It felt good, but I wouldn't put it in my top five."
Importantly, though, it put the Nationals ahead early.
"When you get Livo a lead, there isn't many better at holding it," Dunn said.
In his previous four starts, Hernandez (10-11) was 1-3 with a 9.70 ERA and opponents had hit .364. But he was razor sharp against Atlanta and supplied all the offense he really needed himself.
Keeping the Braves off balance with a variety of pitches, Hernandez gave up just five hits over eight innings and allowed them to get a runner to second base only once.
"He was just so good today," Riggleman said. "He reminds us over and over that it's not about the radar gun and stuff. It's a great lesson for everyone on the staff to watch how he works."
Hernandez said he felt great in the bullpen warming up and expected to pitch well. But he was bothered by a stiff neck in the first inning and had it worked on. After that there was no problem, although watching Dunn's homer caused everyone to crane their neck.
The first baseman's blast cleared the pavilion seats and landed on the plaza area to the right of dead center field. It seemed to hit well past a marked that read 460 feet.
Hernandez had a RBI double to follow Dunn's drive and hit his 10th career homer in the fourth. The pitcher's shot on a hanging 2-2 curve wasn't hit nearly as far as Dunn's, the ball hitting the top of the left-field fence and skipping over.
"I know he can hit," Dunn said. "I see it all the time in batting practice. I'm disappointed it took him this long to get one [this season], to be honest with you."
Jurrjens, who came in 6-1 at home this season, allowed nine hits while falling to 7-6 and worked just five innings after going only 3 2/3 innings in his previous start against St. Louis.
The Nationals, who were shut out in the opener and had scored just 10 runs during the six-game skid, had 11 hits and added a third homer in the ninth as Desmond connected for his 10th off reliever Scott Proctor.
Sean Burnett pitched the ninth for the Nationals and struck out three. He has seven straight scoreless outings.
Fans remember Hernandez's 15-strikeout effort for the Marlins against the Braves in the deciding game of the 1997 National League Championship Series. But maybe as payback for benefiting from umpire Eric Gregg's wide strike zone that day, the native of Cuba didn't have much regular-season luck against the Braves and once lost 11 decisions in a row.
That futility turned last season, though, and Hernandez was 3-1 with a 3.28 ERA in his past six games against the Braves entering Tuesday, although just 6-16 lifetime in the regular season.
It was Hernandez's 20th quality start and he reached the 30-start mark for the 13th straight season.
"You never know what's coming at you," Braves first baseman Derrek Lee said. "He's from 60 mph to 85 mph."
The victory evened the Nationals' record at 7-7 against the Braves and dropped Atlanta two games behind first-place Philadelphia in the National League East.
The Braves are 52-22 at home and have lost just one series all season. The Nationals, playing the role of spoilers, can double that with a win in the rubber game Wednesday afternoon.