Gonzalez hit a two-run blast in the second to put Atlanta in front, Freeman added a solo shot in the fifth and Hinske's two-run homer in the eighth gave the Braves a 5-1 lead.
The Phillies have lost twice in a three-game span and their lead in the National League East was reduced to two games over Florida.
Philadelphia closed within 5-2 going into the ninth and put two men on base in the inning with one out against Craig Kimbrel.
Kimbrel then struck out Shane Victorino and got Placido Polanco on a fly to center to earn his eighth save.
Jair Jurrjens (4-0) allowed a run on eight hits over 6 1/3 innings to get the win. The first two Atlanta homers came against Cole Hamels (4-2), who struck out nine but took the loss in a seven-inning performance.