Cole Hamels, Jake Diekman, Ken Giles and Jonathan Pabelbon combined to strangle the Braves, while Ben Revere had five RBIs at Turner Field.
Hamels struck out seven in six innings pitched, while Diekman, Giles and Pabelbon all dominated an inning each - Giles struck out three from three - to earn the momentous win for the Phillies.
It will mean little for Philadelphia's season, as they remain bottom of the National League's East division, but rivals Atlanta are seven games back from the leading Washington Nationals.
The Nationals increased their buffer courtesy of a 6-4 win over the Los Angeles Dodgers.
Denard Span struck two homers for Washington, as they continued to close on the divisional title.
The Miami Marlins are third, 5.5 games behind the wildcard spots, after a 9-6 win over the New York Mets.
For the first time in 2014, the St Louis Cardinals are outright leaders of the NL Central division, as they downed the Pittsburgh Pirates 5-4 while former pace-setters the Milwaukee Brewers lost again.
The Brewers fell to their sixth-straight defeat, slumping against the Chicago Cubs 4-2, and now sit one game behind the Cardinals.
In the NL West, the Dodgers remain two games clear after the San Francisco Giants were edged 10-9 by the Colorado Rockies.
Charlie Blackmon struck a walk-off single for the Rockies, who came from five runs down through five innings.
The San Diego Padres downed the Arizona Diamondbacks 3-1.
In the American League, East leaders the Baltimore Orioles were humbled 6-4 by the Minnesota Twins.
Baltimore's lead is still a healthy 8.5 games over the New York Yankees, who were not in action.
The Tampa Bay Rays inflicted a 4-3 defeat on the Boston Red Sox, while each of the AL Central-contending Kansas City Royals and Detroit Tigers won.
The Royals, half a game clear, were 4-3 winners over the Texas Rangers, while Detroit thrashed the Cleveland Indians 12-1.
In the AL West, the Oakland Athletics won to consolidate their standing in the wildcard positions, with a 6-1 victory over the Seattle Mariners.