Upset after being spiked high on his leg by Washington's Jose Guillen in the sixth inning, Jones accused Guillen of "a dirty play" and threatened retaliation when the teams play again.
The Braves opened a three-game lead over the Nationals in the division after they were tied entering the three-game series.
The Nationals were trying to rally from an early 4-0 deficit in the sixth when Guillen's single drove in Jose Vidro, who led off the inning with a double. Guillen moved to second on a single by Nick Johnson but was thrown out at third when catcher Brian McCann
fielded a bunt by Vinny Castilla and threw to Jones.
As Jones was awaiting the throw from McCann, he had his back to Guillen, who slid with his cleats high, tearing Jones' pants. Jones said he initially did not know he had been spiked.
"I didn't know what had hit me, I just knew it was high and hard," Jones said. "I turned around and said 'What's up with that?' and he immediately started apologizing. It's kind of hard to deck a guy when he is apologizing."
When it was suggested Guillen and the Nationals were frustrated, Jones said: "The next time I get frustrated, I'll try to take it out on their best player and see how he feels about it. ... We'll see what happens the next time we play them."
Jones, who stayed in the game, said he had a minor cut on his leg.
The teams meet in a four-game series in Atlanta from Aug. 29-Sept. 1.
Guillen said he was just trying to prevent a double play and didn't think he did anything wrong.
"Wait until next time and I'll show you what a dirty play is," Guillen said when told of Jones' comments.
Francoeur, who had three hits and drove in the go-ahead run with an eighth-inning double Wednesday night, had his first multihomer game as he continued to establish himself as a regular in the Braves' lineup.
Francoeur, called up from the minors on July 7, is hitting .441 with five homers and 12 RBI in 12 games.
"I'm working real hard on trying to stay focused and having good at-bats," Francoeur said.
Francoeur's first homer of the game sparked a three-run fourth inning. He added another homer in the sixth inning off reliever Sunny Kim.
"They said he couldn't hit the ball inside, but he went inside and got it," Nationals starter Ryan Drese (3-4) said of Francoeur's first homer. "You have to tip your hat to him. He hit the ball well."
The loss dropped Washington into a tie with Houston for the lead
in the wild-card race after the Astros beat the New York Mets 3-2
Vidro hit a two-run homer, his sixth, for the Nationals, who are only 6-16 since leading the NL East by 5½ games on July 2.
"There was no reason for us to get swept," Guillen said. "We've been letting a lot of people down -- ourselves, our fans, the front office. There's no excuse for the way we've been playing."
Ryan Langerhans followed Francoeur's first homer with a double. After Drese walked Furcal, Giles hit a two-run double to center.
Furcal led off the third with a triple to right and scored one out later when third baseman Castilla fielded a grounder by Jones and threw to the plate. Catcher Brian Schneider missed the throw for an error, giving the Braves a 1-0 lead.
Pinch-hitter Carlos Baerga's bases-loaded infield hit drove in Nick Johnson in the fifth for Washington. The Nationals added a second run in the sixth when Vidro doubled and scored on Guillen's single to right.
Francoeur's second homer pushed the Braves' lead to 5-2, but the Nationals pulled within 5-4 with Vidro's two-run homer off Jim Brower in the seventh inning.
Castilla snapped an 0-for-18 slump with a second-inning infield single. ... Nationals manager Frank Robinson came out for a long argument with plate umpire Gerry Davis after the first pitch from Powell in the sixth inning. On Tuesday, Robinson showed reporters a DVD of Powell's delivery, in which Powell picks up his right foot twice before throwing a pitch. Robinson believes Powell balks before every pitch, but Davis was not swayed by the argument.