A red card for Joel Obi and a dubious penalty decision in the 43rd minute helped Walter Mazzarri's side on their way to all three points as Claudio Ranieri saw his side lose for the first time since he took charge.
Marek Hamsik missed the spot-kick but Hugo Campagnaro scored the rebound and further goals from Christian Maggio and Hamsik in the second half earned Napoli all three points.
The result took them two points clear at the top and left Inter just one point above the bottom three.
Diego Forlan sent in the first shot of the game in the 13th minute, but his 30-yard effort was slightly off target to the right of the goal.
Giampaolo Pazzini had the ball in the back of the net in the 24th minute, but the goal was rightly ruled out for offside.
The complexion of the game then changed with a controversial decision in the 43rd minute.
There was no doubt about Obi making contact with Maggio as he entered the penalty area, but the foul appeared to have been committed outside the box.
The referee Gianluca Rocchi thought differently, though, and pointed to the spot, showing Obi a second yellow card to reduce the home side to 10 men.
Hamsik's penalty was pushed away by Julio Cesar, but Campagnaro was the first to the loose ball and he beat the Inter goalkeeper inside his near post.
Inter's players were infuriated by Rocchi's penalty decision and no fewer than four yellow cards were shown in the last few minutes of the half, with Ranieri being sent to the stands as he confronted Rocchi at the interval.
Inter simply did not have the strength to make a fight of it in the second half with one man less and Napoli took control of the game.
Maggio doubled their lead in the 56th minute when he stole in to take advantage of confusion between Yuto Nagatomo and Julio Cesar, and he lifted the ball into the unguarded goal.
Juan Zuniga somehow lifted the ball over an open goal from six yards in the 66th minute before Hamsik, who had created that chance, added the third.
He latched onto a pass from Ezequiel Lavezzi and made no mistake with just Julio Cesar to beat.