The Nerazzurri faced stiff resistance before winning this quarter-final match.
The match was played at a neutral venue as the Stadio Giuseppe Meazza was being prepared for the opening of the Winter Olympics.
Inter took a two-goal lead through Ange-Yoan Bonny and Andy Diof before Torino reduced the deficit through Sandro Kulenovic.
The Nerazzurri advance to the semi-finals to face the winner of the other quarter-final between Napoli and Como, according to the official Legaserie a website.
The first golden opportunity came in the 20th minute through Carlos Augusto's long-range shot which hit the Torino crossbar.
