Edinson Cavani scored twice to give Napoli, who host Chelsea in a Champions League first knockout round first leg on Tuesday, a 3-0 win at Fiorentina in the other Serie A game.
Inter, who have taken one point from their last 15, dominated much of the game but were caught three times on the break by a side who are a lowly 16th in the 20-team table.
The match ended with deafening jeers and a chorus of 'Jose Mourinho', the coach who led Inter to a Serie A, Champions League and Italian Cup treble two seasons ago, from the Curva Nord's hardcore fans.
"I expected a tough match but not that tough," said coach Claudio Ranieri. "This is an unusual period where we have to accept our responsibilities.
"Apologies to our president and our fans who supported us while the score was 2-0."
Inter's previous sequence of seven wins in a row, including a 1-0 victory over rivals AC Milan in January, is now a distant memory.
Diego Forlan, standing in for Diego Milito in attack, had another unhappy evening as he continued a hapless first season with Ranieri's side.
The low point of Inter's evening came one minute later when Ranocchia tried to chest down a long ball only for Di Vaio to steal in to grab the second goal.
Napoli goalkeeper Morgan Di Sanctis's run of 99 consecutive Serie A games was ended by the flu but it mattered little as Cavani game them a third-minute lead at Fiorentina.
