"You're going to have to win games in hostile environments," Jones said.
Troy Glaus started the decisive rally in the 10th with a leadoff single off Matt Capps (0-1). Melky Cabrera's sacrifice sent pinch-runner Brandon Hicks to second before Diaz, who was hitting .185, looped an opposite-field single to short right.
Hicks scored easily when Roger Bernadina double-clutched and his throw home was late.
"It was a battle, and to win a battle on the road is big," Diaz said. "It's no secret we were struggling a little on the road. That's an understatement."
Braves manager Bobby Cox was rewarded for sticking with the struggling Diaz.
"I had a hunch Matty's going to get hot," Cox said. "He's a hitting machine. He just hasn't got it going, but he will."
Bernadina blamed his hesitation on momentary indecision.
"I should have gone to second," he said. "That ball wasn't hit right at me, so I had no chance to throw [Hicks] out."
Atlanta's road losing streak was its longest since a 10-game skid from Aug. 31 to Sept. 14, 1996.
"We haven't been out there shaking hands much, but we have won four out of five," Cox said.
Braves right fielder Jason Heyward left the game in the second inning with a right groin strain and is day to day. Heyward hurt himself backing up center fielder Nate McLouth on Ryan Zimmerman's sacrifice fly in the first.
"I don't know what I did. I couldn't tell you, to be honest," Heyward said. "When I got back to my position, it felt sore."
The Nationals tied it at 6 against Takashi Saito in the eighth. Ian Desmond reached on an error, Bernadina doubled over Diaz's head in right and pinch-hitter Josh Willingham had a two-run single to left.
Omar Infante's two-run shot put the Braves ahead in the second.
Desmond's homer to left tied it in the bottom half. Bernadina followed with a single, advanced to second on Luis Atilano's sacrifice and scored when Morgan looped an RBI double to left for a 3-2 lead.
In the third, Jones had an RBI single to right, and Glaus' run-scoring groundout snapped the tie in the fifth.
The lead was short-lived. Ivan Rodriguez had a run-scoring single to make it 4-all.
Atlanta went ahead in the sixth, knocking Atilano from the game. Diaz led off with a double and Infante walked before McLouth hit a tiebreaking double to right off reliever Sean Burnett. Prado's groundout then scored Infante for a 6-4 lead.
Atilano, a former Atlanta farmhand making his third major league start, yielded seven hits and six runs in 5 1/3 innings. He walked five and struck out four and said he was a little nervous about facing his former club.
"I was a little pumped up. Obviously, I want to beat them," said Atilano, who was acquired from Atlanta for Daryle Ward in a trade Aug. 31, 2006. "But things happen."
Braves starter Tommy Hanson allowed four runs on nine hits in six innings.
The Braves placed right-hander Jair Jurrjens on the 15-day disabled list with a left hamstring injury, purchased the contract of right-hander Craig Kimbrel from Triple-A Gwinnett and announced that Medlen would start Saturday at Philadelphia in Jurrjens' place. ... Washington still hasn't settled on a substitute for left-hander John Lannan, who will miss Saturday's home start against the Florida Marlins after receiving a cortisone injection in his sore left elbow. ... Nationals right-hander Jason Marquis threw off a mound Wednesday, the first step in his return from inflammation in his right elbow caused by bone chips. He was placed on the 15-day DL on April 21. ... Cox said he may give McCann, who is in a 6-for-31 slump, a day off in Thursday's series finale.