The Partenopei cemented their European status after running riot over Andrea Stramaccioni's injury-ravaged side
The Uruguayan opened the scoring on three minutes but Ricky Alvarez levelled for the visitors from the penalty spot, before Serie A's top goalscorer scored his second and third to put his side out of sight.
The result secures a top three finish for the Partenopei, meaning they are now certain to play in Europe's elite competition next season.
Napoli started brightly and with three minutes gone Goran Pandev set Cavani free and the striker produced a masterful finish to slot the ball home. Despite the set-back, the visitors came close to mustering a rapid fight-back, with Fredy Guarin's free-kick and then Alvaro Pereira's smart turn and shot drawing difficult saves from Morgan De Sanctis.
Inter's endeavour was soon to pay off though, as a slick Mateo Kovacic ball found Alvarez advancing into the Napoli area, only to be barged down by the retreating Juan Zuniga. Alvarez picked himself up and promptly buried the spot-kick into the corner for a deserved 23rd minute equaliser.
Guarin tried once more to fire his side into the lead when he cut in from the flank and tested De Sanctis from an acute angle, but Samir Handanovic also had to be alert at the other end to thwart Blerim Dzemaili, who attempted to extend his recent hot-scoring streak with a rising shot.
Zuniga eventually made up for his earlier mistake when he was brought to a crude halt by Jonathan in the Inter box. Cavani lined up the resulting penalty and made no mistake from 12 yards for his 100th goal in Napoli colours.
Despite further penalty calls from Guarin and Zdravko Kuzmanovic, it was Handanovic who had to stay alert to keep out Hamsik before the half-time whistle brought a halt to proceedings.
Andrea Ranocchia headed wide from a corner kick just after the restart and Cavani slashed a shot beyond the woodwork in a lively start to the second period.
The in-demand striker was to make amends shortly after, though. Pandev made inroads down the left again before swinging the ball into the centre, which a rash Handanovic completely misjudged, leaving Cavani with the simplest of tap-ins to spark rapturous celebrations from the Napoli faithful.
With the wind taken from their sails, Inter barely troubled Walter Mazzarri's men thereafter as supporters of the Naples club began to celebrate a guaranteed top-three finish and Champions League football next season.
For Inter, their ninth away loss of the season leaves them in an underwhelming eighth position as their campaign goes from bad to worse.