Pettibone (5-3) yielded just one run on five hits en route to the victory, his second in two starts. The rookie right-hander issued one walk and struck out six.
Brown gave the Phils a quick lead with a first-inning RBI triple and then came home on a Delmon Young single to make it 2-0.
His solo homer in the fifth padded Philadelphia's lead to 5-1.
Ben Revere drove in a pair of runs with a three-bagger as Philadelphia claimed the rubber match of a three-game series.
Braves starter Kris Medlen (6-8) was scorched for seven runs (six earned) on eight hits in a 5 1/3-inning effort.
Celebrity Families of 2014 [PHOTOS]