The pair took their fine club form onto the international stage in Natal as the South American heavyweights extended their winning run to three games.
Neymar opened the scoring before Coutinho grabbed a second, coolly controlling a pull-back inside the area and prodding a finish into the bottom corner.
Further strikes from Filipe Luis and Gabriel Jesus had the Brazilians 4-0 ahead at half-time, and Firmino was then introduced to the mix on 67 minutes.
The Liverpool No.11 wasted little time in adding his name to the scoresheet either, reaching a back-post corner from Coutinho to nod a header home for the fifth.