Minor (6-7) retired the final 13 batters he faced after allowing a fourth-inning homer to Chase Utley, breaking a two-game personal winless streak.
The left-hander yielded four hits, didn't issue a walk and struck out nine as Atlanta -- which came into the contest holding the second National League wild card spot -- won its fourth straight.
Joe Blanton (8-9) took the hard-luck loss for the Phillies, yielding two runs on four hits over seven frames. He struck out seven.
Celebrity Families of 2014 [PHOTOS]