Just two weeks after beating champions AC Milan 3-1 at home, Walter Mazzarri's team took another impressive scalp.
Hugo Campagnaro, Christian Maggio and Marek Hamsik scored the goals while Inter's Joel Obi and coach Claudio Ranieri both saw red.
Ranieri was furious with referee Gianluca Rocchi.
"He wasn't equal in his decisions, it was an unfair game," he said. "The first half was a great game but Obi was given a first yellow card when he clearly won the ball.
"Then (the foul) was outside the area and he was given a second yellow card and he was off. That ruined the game.
"It's a shame because we tried very hard but (the referee) messed up everything there was to mess up."
Mazzarri, however, insisted his side deserved to win.
"We played very well, we deserved to win. Against Fiorentina (a 0-0 draw) there was a clear penalty that wasn't given, against Milan last season there was a dubious penalty (to Milan) and we lost," he said.
"Everything can happen, everyone can say something, we don't talk about the penalty against Fiorentina so don't talk about today's incidents."
Napoli fought for the title last season but missed out as they picked up only one point in four games against their two Milanese scudetto rivals.
But already this season they have shown they are a different proposition and ahead of Sunday's games, are back on top while Inter languish down amongst the basement sitters.
There were few chances until an explosive incident just before the break.
Obi pushed Maggio as he was storming into the box and the referee pointed to the spot.
Obi was already on a yellow card as he'd been booked for a foul on Ezequiel Lavezzi, although television replays showed he clearly won the ball.
Television replays also showed his push on Maggio was outside the box but the referee gave a penalty while showing a second yellow card to the Nigerian.
With Obi trudging off the pitch, Inter goalkeeper Julio Cesar saved Hamsik's penalty but Campagnaro was the quickest to the rebound and slammed home at the near post.
That sparked a period of irritation in which Inter captain Javier Zanetti and Cesar were both booked for angrily confronting the referee while Ranieri was given his marching orders for doing likewise at the break.
Napoli put the game to bed 11 minutes into the second period when Maggio made another burst from deep and although Japanese full-back Yuto Nagatomo was ahead of him, he hesitated as Cesar came out, allowing the Napoli wing-back to stretch out a leg and lob the goalkeeper.
Juan Zuniga should have added a third from Hamsik's tee-up but somehow skied the ball from eight yards with an open goal to aim at.
However Walter Gargano then played in Hamsik 15 minutes from time and the Slovakia midfielder finished with aplomb.
Earlier in the day Roma moved up amongst the leaders after recording their second straight victory with a 3-1 success over previously unbeaten Atalanta.
Bojan Krkic and Pablo Osvaldo gave Luis Enrique's team a 2-0 half-time lead and although German Denis pulled a goal back early in the second period, Brazilian Simplicio sealed the three points late on.
Having taken over the club in the summer Enrique needed six games to finally register a win but at the Stadio Olimpico the team looked like they were finally starting to gel.
"Today I was happy with the approach and the behaviour of the team," he told Sky.
"This is the football I want to see with lots of possession leading to attacks and chances."
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