Hampton (3-3) gave up two runs on six hits and three walks for Atlanta, which has won three of four. It was Hampton's first win since Aug. 16, as he went 0-2 in six starts in between.
Kelly Johnson also had an RBI hit in the win for the Braves.
Losing pitcher Cole Hamels (14-10)struggled through the early innings. He gave up three runs on eight hits and a walk in seven innings while striking out seven.
The Phillies saw their lead in the National League East fall to 1 1/2 games over New York after the Mets won Tuesday. Philadelphia's magic number to clinch the East stayed at four. Pat Burrell and Pedro Feliz each had an RBI for the Phillies.