The home side, roared on by a packed San Paolo stadium, took the lead within three minutes.
Inter goalkeeper Julio Cesar was forced to rush from his goal to make a hurried clearance but could only direct the ball to Marcelo Zalayeta who lobbed into the empty net.
Ezequiel Lavezzi was causing the Nerazzurri all sorts of problems with his mazy runs.
After firing just wide, the Argentine striker nearly caused Marco Materazzi to put through his own net but Julio Cesar clawed the ball off the line.
Napoli poured forward after the break and only a sharp save kept Marek Hamsik from doubling the scoreline.
Zalayeta missed a golden opportunity to increase the lead when Julio Cesar saved the Uruguayan's penalty after the keeper was adjudged to have tripped midfielder Walter Gargano.
The defeat means that Inter's lead has been reduced to six points over AS Roma.
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