Brown's blast in the third inning erased a 2-0 deficit and his run-scoring walk triggered a three-run outburst in the fifth that iced the contest for Philadelphia.
Brown finished with four RBI while John Mayberry also drove in a run as Philadelphia rebounded from a 4-3 loss in Monday's opener of a three-game series.
Kendrick (7-4) broke a personal three-start winless streak, allowing two runs on seven hits in eight innings. The right-hander didn't issue a walk and struck out six.
Pedro Ciriaco and Alexi Amarista each drove in a run for the Padres.