A place in the final to face Juventus on Wednesday was up for grabs, as Inter gave a start to January signing Christian Eriksen while Napoli gave Matteo Politano starting against his parent club.
Inter were off to a fiery start after Eriksen nestled the bottom corner from a direct corner kick three minutes into the contest.
With 20 minutes gone, pressure play from Napoli almost resulted in the equaliser with Samir Handanovic forced to clear away after being pressed by Politano.
A one-handed save from David Ospina a little after the half-hour mark denied Romelu Lukaku, who had gotten on the end of Ashley Young's cross.
Ospina got to work again after a mazy run down the right by Antonio Candreva ended with a snap-shot which the Colombian palmed for a corner five minutes to halftime.
Napoli drew level three minutes later after a route one from Ospina released Lorenzo Insigne who fed Dries Mertens to turn home and become the club's all-time leading scorer.
In the second half, Napoli went close to a second goal after Mertens delivered a ball to Insigne, who flashed wide of Handanovic's goal.
The Napoleons introduced a double change just after the hour mark in Jose Callejon and Fabian Ruiz, with Politano and Eljif Elmas making way in the process.
Eriksen searched for his second goal of the evening from a free-kick with 12 minutes remaining, but Ospina pushed across to parry.
The Nerazzurri pushed for the all-important second, but it wasn't to be as Napoli advanced to Wednesday's final against Juventus.