Firmino, a 61st-minute substitute, burst clear after 73 minutes and expertly rounded Chile keeper Claudio Bravo before dispatching a simple finish into the empty goal.
Brazil forward Neymar and Chilean Alexis Sanchez were the standout players for their sides but were often wasteful after dazzling build-up play in a full-blooded game that was punctuated by a host of fouls and heavy challenges.
Brazil, who beat France 3-1 last week, have won all eight matches under coach Dunga since finishing fourth as hosts at last year's World Cup.
They have now lost just seven times in 70 games against south American rivals Chile.