The Braves, who are steamrolling to an almost certain National League East title, lost their second in a row.
Atlanta scored in the third on a leadoff home run by Andrelton Simmons that spoiled an otherwise tremendous outing by Cliff Lee and the Braves protected their narrow advantage until the Phillies staged a two-out comeback in the seventh.
Darin Ruf reached with a single on a 3-2 pitch and Asche followed by hitting the first offering from Mike Minor over the wall in right. The home run came in Asche's 30th major league game and 101st career at-bat.
Lee (12-6) worked eight innings for the win, giving up just two hits without a walk. He struck out 10. Jonathan Papelbon survived a two-out single in the ninth for his 25th save.
Minor (13-6) suffered the hard-luck loss after surrendering only four hits in seven innings and striking out nine.