Torino entered the match off the back of successive wins in Serie A, and a strong start to their league campaign has left them in eighth position in the table.
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It did not take long for the hosts to take control of the contest, with Alessandro Gazzi opening the scoring in just the third minute.
The Serie A outfit continued to dominate matters in the early stages and had their second in the 13th minute when Emiliano Moretti found the back of the net.
Cesena, who were relegated from Serie A last season, improved at the start of the second period, but the game was put beyond them in the 51st minute when Maxi Lopez made it 3-0 to the home team.
Thirty-two-year-old midfielder Emmanuel Cascione had one back for Cesena in the 68th minute as the Serie B outfit threatened a late comeback, but Torino added a fourth late on through Marco Benassi as they booked their spot in the round of 16 in routine fashion.