Marek Hamsik should have done better for the hosts on 15 minutes, but the forward could only put his headers from Ezequiel Lavezzi's cross over the bar.
Napoli had another great chance almost instantly when Christian Maggio inexplicably fired over the bar with just Luca Castelazzi to beat.
As they controlled the first half, the hosts could have had a penalty when Christian Chivu appeared to barge Edinson Cavani over in the box. However, the referee waved away the Napoli appeals.
The home side were awarded a spot kick early in the second half as Thiago Motta brought down Cavani just as the striker was about to shoot. Cavani dusted himself off to take the penalty and send the goalkeeper the wrong way.
Inter were nearly awarded a spot kick on the hour, but Diego Milito was booked by the referee following a challenge by Maggio.
Wesley Sneijder came within inches of an equaliser for Claudio Ranieri's side, but his shot curled the wrong side of the post in a frantic final ten minutes.
Maicon was almost the unlikely source for an Inter leveller as his cross nearly found the net. However, Morgan de Sanctis was able to tip the ball over.
As the Nerazzuri surged forward, Napoli sealed the win in injury time when Cavani finished off a counter-attacking move.