The 19-year-old exhausted the entire duration of the game to mark his first full match for the former Italian champions.
Duncan who has been capped once by Ghana in a friendly match was promoted to the senior team at the start of the season.
The young midfielder told the Inter Milan website after the match that he was excited to have played a significant role to help a 10-man Nerazzurri to win the game against the Serie B campaigners.
“It was crucial to win today, so I'm very happy," Duncan told Inter.it. “Everyone helped me today, especially the defence who told me where I needed to be."
"It was great, I dreamt of playing at the San Siro and as soon as I saw the fans I felt excited.
“I'm improving tactically and in terms of my positional sense,” he added.
Inter will face either Napoli or Bologna in the last eight next month.