Atlanta has cleared that hurdle with six straight wins over the Phillies this month.
Jones and Jason Heyward homered off Roy Halladay, and the Braves completed a three-game sweep of last-place Philadelphia with a 6-2 victory Sunday.
Atlanta also swept a three-game series at Philadelphia from July 6-8. The Braves have won six straight over the Phillies for the first time since 1996-97, according to STATS LLC.
"It's a big, big sweep for us," Jones said. "I think mentally as a team you've got to get over certain humps, and Philly as a team has been a big hump for us. They've been winning the division for a long time and they've handled us pretty well. Now we've got to get over that hump of beating the Nationals. The Nationals have had our number a little bit the last couple of years, and they're the team ahead of us, so we have to get going."
Atlanta, which remained four games behind first-place Washington in the NL East, has won five straight.
Tim Hudson (10-4) gave up two runs and seven hits in 5 2-3 innings and combined with Ben Sheets and Mike Minor to give Braves starters four runs and one walk allowed in the series.
Hudson has reached 10 wins despite missing most of the first month while recovering from back surgery. He is 4-0 with a 3.19 ERA in his last five starts.
"I've been fortunate to be able to go out there and stay healthy since I missed that first month," Hudson said. "Guys have played really well behind me. Every time I've gone out there we've scored runs. It's easy to get wins when they score five or six runs for you."
Jonny Venters, Chad Durbin, Eric O'Flaherty and Cristhian Martinez followed with two-hit relief.
With the Braves ahead 3-2, Freddie Freeman hit a two-run single off Jake Diekman in a three-run seventh.
In danger of ending a streak of consecutive playoff appearances at five, Philadelphia (45-57) is last in the NL East this late in a season for the first time since Aug. 12, 2002, STATS said. The sweep could turn the Phillies into sellers before Tuesday's deadline for trades without waivers.
Shane Victorino, Hunter Pence and Joe Blanton have been mentioned in trade speculation. Victorino and others lobbied after the game for management to keep the team intact.
"We've got 60 games," said Victorino, who homered and had three hits. "That's my goal, to play 60 games here. I'm wearing a 'P' on my hat, 'Phillies' across my chest. I want it to be here."
Asked whether the Phillies will be buyers or sellers at the trade deadline, manager Charlie Manuel said: "I think where we're at speaks for itself.
"We're definitely behind. We would have to come a long way. ... We've still got a heartbeat."
Braves manager Fredi Gonzalez said the Phillies remain a dangerous team.
"They're a good club, and they still scare you," Gonzalez said. "They're not clicking on all cylinders right now for whatever reason. But they still have got a pretty good pitching staff and they've got those guys in the middle of the lineup.
"They're still a respectable team and I still respect them, just for the fact they're a veteran group of guys that have won championships and a World Series. To me it's just a matter of time before they get it going."
Halladay (4-6), a two-time Cy Young Award winner, allowed three runs and six hits in six innings with seven strikeouts, dropping to 0-1 with a 5.82 ERA in three starts after missing seven weeks with a strained right lat muscle. He got his 2,000th strikeout in the first inning, fanning David Ross.
Atlanta took a 2-0 lead in the first as five straight hitters reached with two outs. Heyward hit a first-pitch homer, his 16th home run of the season, and Dan Uggla stopped an 0-for-21 slump with an RBI double.
Jones led off the third with his 10th homer, pushing the lead to 3-0. He has 1,042 extra-base hits, passing Pete Rose for sole possession of second place for switch-hitters, behind Eddie Murray's 1,099.
Victorino led off the fourth with his ninth homer and Carlos Ruiz knocked out Hudson with an RBI single in the sixth.
Diekman dropped Heyward's grounder for a run-scoring error in the seventh.
NOTES: Gonzalez expects SS Andrelton Simmons, who was placed on the 15-day DL with a broken right little finger on July 13, to need six weeks to recover, including an injury rehab stint. That would place his return around Aug. 24. ... Laynce Nix made his first start of the season in right field. Hunter Pence, who had started 100 of the first 101 games in right field, remained in right field after his pinch single in the sixth. ... The Phillies are off Monday and open a series at Washington on Tuesday night with LHP Cliff Lee on the mound. Braves RHP Tommy Hanson will face Miami LHP Mark Buehrle in the opener of a four-game series on Monday night.