Fredy Guarin and Diego Milito got the goals for Andrea Stramaccioni's side, who were grateful for a profligate Napoli performance.
Edinson Cavani did get a goal back for the visitors, but they paid the price for poor finishing and misfortune in front of goal as they relinquished second spot and fell five points behind Juventus, with Inter one point above them.
Guarin was left totally alone at the far post to meet a corner and beat Morgan De Sanctis after racing into the penalty area from deep as Inter took an eighth-minute lead.
Christian Maggio should have levelled immediately for Napoli, but he lacked the adroitness shown by Guarin and blazed the ball over the crossbar from close range with only Samir Handanovic to beat.
Napoli went even closer to levelling in the 18th minute when Cavani set up Lorenzo Insigne for a shot which only just went wide of the post with Handanovic beaten.
Marek Hamsik was next to go close as Napoli searched for an equaliser.
In the 28th minute Cavani should have found it, but he missed the target with a header from just six yards out as it started to look like it was not going to be Napoli's night.
That certainly looked the case when Milito doubled Inter's lead in the 39th minute with a shot into the far corner which De Sanctis, despite making contact, was unable to keep out.
It was almost three in the 52nd minute when Antonio Cassano's shot hit the post while Gokhan Inler tested Handanovic shortly afterwards.
Napoli finally got the goal they were looking for in the 54th minute when Cavani completed a move which summed up their night.
Goran Pandev's effort was saved by Handanovic with Maggio hitting the rebound against the crossbar. His second attempt was saved instinctively by Handanovic before the Uruguayan lashed home the loose ball.
Napoli surged forwards in search of an equaliser which they almost got in the 85th minute when Cavani's dangerous low cross was nearly turned into his own goal by Alvaro Pereira, but Inter survived that late scare to hold on to the victory.