The switch-hitting Jones was swinging as a left-handed hitter when he saw three straight fastballs from Papelbon. Jones pulled the third pitch deep into the right-field seats.
Then came the celebration every player cherishes - none more than the 40-year-old Jones, who is retiring after the season.
''In that mob scene at the plate, you kind of get lost in it, time kind of stands still,'' Jones said. ''You're not really thinking about any of that other stuff. You're just thrilled that you won a game.
''Nothing beats that. That's as good as it gets.''
Jones has two game-ending homers this season, both against the Phillies. On May 2 in Atlanta, his 11th-inning, two-run shot gave the Braves a 15-13 win.
This win was more important, because the Braves appeared bound for their fourth straight loss. There was growing talk the team could stage of repeat of its collapse in September of 2011 when it blew a wild-card lead. The 2011 collapse ended with three straight home losses to the Phillies.
Talk of another September failure would have grown if the Braves had been swept. Instead, they boosted their status as the NL wild-card leader.
''This is something I think we need right here,'' Braves manager Fredi Gonzalez said. ''This is something to get the team going again and get the juices flowing again.
''He came through again. ... It's unbelievable.''
The Phillies led 7-1 after three innings and carried a four-run advantage into the ninth.
The Braves rallied against Jeremy Horst and Papelbon (3-6).
Reed Johnson singled off Horst with one out for his third hit and Paul Janish walked. Papelbon struck out pinch hitter Lyle Overbay before walking Michael Bourn to load the bases.
Martin Prado's grounder skipped past third baseman Kevin Frandsen for a two-run double, setting the stage for Jones' 14th home run.
The blown save was the fourth in 35 chances for Papelbon, who said he didn't regret throwing three straight fastballs.
''I threw the pitch I wanted,'' Papelbon said. ''I'm the pitcher. I throw the pitch I want.''
The Phillies would have climbed to within four games of .500 and within seven games of the wild-card leaders with a win. Instead, they could only stare as Jones circled the bases.
''It was sitting right there for us,'' Phillies manager Charlie Manuel said. ''We couldn't finish it off.''
''It was set up perfect for us. We didn't get it done. ... We won the series but so what? We had a chance to sweep. We need to win every game we can. ''
Papelbon refused to overstate the impact of one loss.
''I wouldn't say it's a crushing loss,'' Papelbon said. ''We've had a lot of losses this year. We've had a lot of chances to sweep teams.''
Peter Moylan (1-0) got one out for his first win in his comeback from a torn right labrum and rotator cuff. He was added to the roster on Saturday.
Eric Kratz hit a three-run double and Ryan Howard drove in two runs with a double as the Phillies took a 5-0 lead against Paul Maholm.
Pitcher Cole Hamels added a two-run double in the third as the Phillies made it 7-1. Hamels gave up three runs on six hits and two walks in six innings.
Maholm left without recording an out in the third inning for his shortest start of the season. He gave up seven runs on six hits and three walks.
The Phillies hit six doubles, including three in the big first inning.
Johnson drove in three runs for Atlanta. He had an RBI double in the second and a two-run single in the sixth.
Bourn made a leaping catch at the center-field wall on a drive by Chase Utley to open the sixth.
NOTES: The Phillies recalled RHP Justin De Fratus and LHP Jake Diekman from Triple-A Lehigh Valley. ... Braves SS Andrelton Simmons, who has been on the disabled list since July 13 with a broken right little finger, will begin a rehab assignment at Double-A Mississippi on Monday. Gonzalez said Simmons could come off the DL as soon as next weekend. ... RHP Kris Medlen will start as the Braves remain home to open a four-game series against RHP Tyler Chatwood and Colorado on Monday. Phillies RHP Tyler Cloyd will face Johnny Cueto and the Reds in Cincinnati on Monday.