The match oN Tuesday was preceded by a tribute to late US basketball legend Kobe Bryant, who lived in Italy as a child and who died in a helicopter crash on January 26.
Players from both sides took to the field with back armbands in a sign of mourning for Bryant, who was a Rossoneri supporter, reports Xinhua news agency.
Milan midfielder Giacomo Bonaventura scored the first goal 12 minutes from kick-off, putting Torino against the ropes psychologically after a disastrous Serie A match that saw it lose to Atalanta 0-7 on January 25.
However, the Granata side remained undaunted, making a comeback with a goal by Gleison Bremer in the 34th minute. The 23-year-old Brazilian defender, who made his Serie A debut with Torino in 2018, followed this up in the second half with a header in the 71st minute.
Just when all seemed lost for the Rossoneri, midfielder Hakan Calhanoglu evened the score with a goal one minute into 5 minutes of extra time.
The match ran into overtime, and Calhanoglu scored again at the 106th minute. Two minutes later, teammate Zlatan Ibrahimovic cinched Milan's victory with a fourth goal.
"This was an important win for us, also because of the way it came - we were down by 2-1 but we were able to believe in ourselves to the end," Milan captain Alessio Romagnoli told RAI Channel 1 public television, which broadcast the match.
Milan will face Juventus in one of the two Coppa Italia semi-finals after Juve bested Roma 3-1 on January 21.
Inter face Fiorentina in the last quarter-final on January 29, also at San Siro in Milan. The winner of that match will face Napoli, which knocked out Lazio 1-0 on January 22.
The semifinals are slated for February and March, with the final to be played May 13.
( With inputs from IANS )