Soriano, who began the ninth with a 6-0 lead, also gave up pinch-hit RBI single to Greg Dobbs and Jimmy Rollins' RBI single before he stranded two runners on Ben Francisco's pop-up.
Martinez (5-1) left his start after three innings because of neck stiffness. The three-time Cy Young Award was trailing 3-0 when he approached the mound to begin warming up for the fourth, but he never got the chance as manager Charlie Manuel brought in Chad Durbin.
Martinez gave up seven hits, three runs and one walk with one strikeout.
Vazquez (14-9) won his third straight start, allowing three hits and three walks with six strikeouts in seven scoreless innings. Lowering his ERA 10 points to 2.91, Vazquez allowed the Phillies to get just two runners in scoring position, neither as far as third base.
Atlanta has won eight of nine and nine of 11. The Braves won a season series over Philadelphia, the defending World Series champion, for the first time since 2004.
Adam LaRoche, who went 2 for 2, made it 1-0 with an RBI single in the second. The Braves led 3-0 in the third on RBI singles by Brian McCann and LaRoche, but Martinez stranded six runners through the first three innings.
Durbin gave up Martin Prado's sacrifice fly RBI to make it 4-0 in the fourth, and Matt Diaz's 11th homer, a two-run shot, that gave the Braves a 6-0 lead in the fifth.
Philadelphia had a 7-0 record in Martinez's seven starts this season. He was coming off a 130-pitch performance that included eight scoreless innings, six hits, no walks and seven strikeouts in a 1-0 victory last Sunday against the New York Mets, his former team.
Martinez, who missed parts of 2007-08 because of reconstructive shoulder surgery with the Mets, was not offered a contract after going 5-6 with a 5.61 ERA in 20 starts last year for New York. The Phillies, who signed him July 15, were the only team to offer Martinez a contract.
Dropping to 3-1 on the road, Martinez's ERA rose 57 points to 5.66 away from Philadelphia. Entering Saturday, Martinez had benefited from the Phillies' offense outscoring opponents 38-19 in his first seven starts.
He was seeking his 12th victory against the Braves, which would've been his most against any other NL club.
Howard, who homered twice in the Phillies' 9-4 victory Friday, is hitting .344 with eight homers and 16 RBIs this year against Atlanta. In his career, Howard has 32 homers, 87 RBIs and a .342 average in 298 career at-bats against the Braves.
Notes: Phillies CF Shane Victorino, who did not play Friday, struck out in a pinch-hit appearance with runners on first and second in the ninth. He had been suffering flu-like symptoms. ... Howard wearing a sleeve on his left forearm after getting hit by pitches in the same spot against Washington on Thursday and Atlanta on Friday. ... Philadelphia C Carlos Ruiz was held out of the Atlanta because of a left wrist sprain.