Stevan Jovetic's stunning second-half strike was the catalyst as Inter saw off Napoli and claimed a place in the last four of the Coppa Italia.
He struck with 16 minutes left at the San Paolo before Adem Ljajic's goal on the break sealed victory - but the game was marred by a touchline spat between Roberto Mancini and Maurizio Sarri.
Inter will now visit the winners of the final quarter-final final tie between Lazio and Juventus, which is played on Wednesday.
Napoli manager Sarri rotated his team and his most notable change saw top scorer Gonzalo Higuain dropped to the bench.
Nevertheless, the hosts began brighter and Dries Mertens drew a good stop from Samir Handanovic, who palmed a decent effort away to safety.
Back came Inter, who almost caught sight of goal only for a defender to block and former Liverpool keeper Pepe Reina to pounce gratefully on the loose ball.
Despite Sarri's tinkering, Napoli played with the confidence which has taken them two points clear of Juventus at the top of Serie A.
Handanovic was well placed to keep out Jose Callejon, albeit his shot was tame after Ivan Strinic picked him out with a cutback from the goal line.
Keeper Handanovic was in the right position once again to deny Manolo Gabbiadini moments later, only for the offside flag to render his efforts unnecessary in any case.
The game continued in much the same vein after the restart, with both sides untidy in possession at times and wasteful in front of goal.
Alex Telles hit the wall with a free kick before Jovetic failed to connect with a Yuto Nagatomo cross as Roberto Mancini's visitors tried to exert extra pressure without any success.
Mertens hit the target with a decent attempt for Napoli but once again he lacked an edge and drove straight at Handanovic.
Jovetic looked like ending the impasse at last as he shot from long range with venom but Reina held his attempt then Gary Medel went close but bent a twisting volley a yard over the crossbar.
Sarri threw on Higuain with 19 minutes remaining and his introduction was the prelude for a goal at last - only it came Inter's way.
Jovetic picked up the ball in a central area and with space opening up in front of him, he sent a dipping shot beyond Reina and inside his left-hand post from 25 yards.
It was a fine strike which belied a poor game overall and Napoli's hopes of an equaliser lessened when Mertens received a second yellow card for simulation in the penalty area.
Inter then made sure of their success in stoppage time as Ljajic raced clear before tucking a composed finish under Reina from the edge of the area.
Mancini missed the goal as he was involved in a heated exchanged with the fourth official and Sarri - whom he later claimed had subjected him to a homophobic slur - and he was consequently sent off too.