Kendrick (6-3) allowed two runs on six hit en route to his fourth career complete game. The right-hander issued one walk and struck out five in the 105-pitch performance.
Brown went 3-for-4 with a two-run blast in sixth inning, giving him nine round-trippers in 10 games and 42 RBI for the season.
Delmon Young and Erik Kratz also went deep for the Phillies, who took the opener of a three-game series.
Miami starter Tom Koehler (0-4) absorbed the loss, surrendering five runs (four earned) on seven hits over five full frames.
Derek Dietrich and Marcell Ozuna each knocked in a run for the Marlins.