Stevan Jovetic, Adem Ljajic scored in the last 20 minutes to send Inter into the semi-finals.
Milan: Inter Milan coach Roberto Mancini missed his team`s second goal as he argued with his opposite number and was then sent off in their 2-0 Coppa Italia win at Napoli on Tuesday.
Stevan Jovetic and Adem Ljajic scored in the last 20 minutes to send Inter into the semi-finals while Napoli had Dries Mertens sent off late in the game for diving.
Serie A leaders Napoli rested topscorer Gonzalo Higuain but Inter`s Samir Handanovic was still the busier goalkeeper, making several last-ditch saves to keep Napoli at bay.
But Inter went ahead when Jovetic curled in a right-foot shot from 20 metres from a counter-attack in the 74th minute.
Mertens was given a second yellow card for a theatrical fall in the penalty area as Napoli pressed for an equaliser, before Ljajic broke clear from the halfway line to score Inter`s second in stoppage time.
Mancini did not see the goal as he became involved in a heated exchange with the fourth official and then Napoli coach Maurizio Sarri, and was ordered from the touchline.
The row appeared to begin after the fourth official mistakenly indicated nine minutes of added time before changing his mind and indicating five instead.
(Writing by Brian Homewood in Berne; editing by Justin Palmer)