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.
Marco Di Vaio netted twice in two minutes just before half-time, the second after a dreadful blunder by Andrea Ranocchia, and Robert Acquafresca made it 3-0 late in the second half.
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.
President Massimo Moratti left his seat 10 minutes from time, before the third goal, as Inter slipped to sixth with 36 points from 24 games while Napoli climbed to fifth on 37.
"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.
Beaten 1-0 at home by bottom club Novara on Sunday, Inter controlled the first half-hour but fell behind in the 37th minute when Di Vaio cut inside his marker and fired a low shot past goalkeeper Julio Cesar.
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.
Bologna goalkeeper Jean Gillet produced some good saves after the break including a superb reflex effort to turn away a Ranocchia header as the defender tried to make amends for his earlier blunder.
Exposed on the break, Inter were caught out again five minutes from time when Acquafresca collected the ball and ran past three defenders to score with a low shot into the far corner.
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.
The Uruguayan struck again 10 minutes after the restart, springing the offside trap and beating Artur Boruc inside his near post for his 15th league goal of the season.
Ezequiel Lavezzi completed the scoring in stoppage time following a counter-attack.
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