Napoli boss Maurizio Sarri opted to make widescale changes to his side, who remain in the hunt for the Serie A title.
The German outfit began the game on the front foot as Werner connected with a corner kick to fire at Pepe Reina early on before rifling wide minutes later.
However, Leipzig could not find a breakthrough and conceded against the run of play when Ounas picked up Marko Rog's pass and dispatched a low drive across goal and into the far corner.
The Leipzig comeback was then complete on 74 minutes as a long ball saw Yussuf Poulsen surge into the penalty box and deliver the ball on a platter for Bruma to tap home unmarked.
Napoli tried desperately to force an equaliser but found themselves on the receiving end of a third goal as Emil Forsberg set up Werner to convert for the third goal of the game.
NAPOLI (4-3-3): Reina; Maggio, Tonelli, Koulibaly, Hysaj (Rui 54'); Rog, Diawara, Hamsik (Insigne 54'); Ounas (Allan 60'), Callejon, Zielinski
RB LEIPZIG (4-4-2): Gulacsi; Laimer, Orban, Upamecano, Klostermann; Sabitzer, Kampl, Keita (Demme 85'), Bruma (Forsberg 79'); Poulsen (Augustin 82'), Werner