Chris Coste, Shane Victorino, Jayson Werth and Jimmy Rollins also went deep for the Phillies, who overcame a 5-0 deficit a day after coming back from a 9-3 hole.
Since June 5, the Phillies are 8-1 against the Braves and 12-22 against everyone else.
"We play well against them, that's for sure," Werth said. "I can't put a finger on it."
Braves All-Star catcher Brian McCann left with a mild concussion after a collision with Victorino in the sixth inning. X-rays were negative and McCann will be re-evaluated Monday.
"I have a headache right now, but I'll be OK," McCann said. "I'm not too worried. I'll probably be out a couple days."
Kelly Johnson and Omar Infante hit consecutive homers in the fourth inning for Atlanta. The Braves scored five times off Rudy Seanez and Ryan Madson in the eighth to make it close, and had the tying run at the plate in the ninth.
"We lose a five-run lead today, a six-run lead yesterday," manager Bobby Cox said. "With leads like that, you think you ought to be able to win."
The game was delayed 1 hour, 57 minutes in the bottom of the second. Neither starting pitcher returned when play resumed.
Clay Condrey (3-2) pitched two scoreless innings to earn the win, and Brad Lidge worked the ninth for his 24th save in as many chances.
Julian Tavarez (0-1) allowed the decisive homer to the first batter he faced.
Johnson ripped a two-run shot to right off Adam Eaton and Infante reached the seats in left to give the Braves a 5-0 lead in the fourth.
But the Phillies answered against Jo-Jo Reyes with two outs in the bottom half. Coste got the rally started with a two-run shot. After pinch-hitter So Taguchi reached on an infield single and Rollins walked, Victorino connected to tie it at 5.
Burrell put the Phillies ahead to stay in the fifth with his 26th homer - a drive into the left-field seats.
"We have a great offensive club," Werth said. "We just haven't been swinging well collectively."
The Phillies tacked on five runs in the sixth. Victorino had an RBI single and Ryan Howard delivered a two-run single. On Howard's hit to right field, Victorino jarred the ball loose when he ran over McCann.
McCann stayed down for a couple minutes, before walking off the field on his own.
"The only way I thought I can be safe was to jar the ball loose," said Victorino, who spoke to McCann after the game. "I play the game hard. I hope he's fine."
Pinch-hitter Martin Prado's bases-clearing double capped a five-run eighth and got the Braves within two.
An animated crowd that mostly stuck around after the rain delay mocked the Braves with a tomahawk chop in the sixth. They saw the Phillies win an important series after falling out of first in the NL East following a 53-day stay atop the standings.
"We never give up. It's fun," Victorino said. "We play 27 outs. We keep fighting."
Phillies starter Joe Blanton allowed two runs and three hits in two innings in his second outing since he arrived in a trade with Oakland.
Braves starter Jorge Campillo gave up two hits in 1 2-3 scoreless innings. Reyes, who was scheduled to start Monday night against St. Louis, allowed five runs and three hits in 2 2-3 innings.
Notes: Braves 3B Chipper Jones remained out of the lineup with a strained left hamstring. Jones, who leads the majors with a .369 batting average, could be headed for the disabled list. ... Phillies 3B Pedro Feliz missed his third straight game with tightness in his lower back. ... The Phillies are 18-6 in the last 24 games against Atlanta, including 10-2 this year. ... Reyes doubled off Eaton for his first hit in 20 at-bats this season. ... The five homers were a season high for Philadelphia.
