It was a replay of the Coppa Italia Final on May 20, which saw Walter Mazzarri's men emerge 2-0 winners.
Marchisio said: "This was a good 'revenge' for that game. It was a tough victory that allowed us to start the season well.
"Once again today we showed character by coming back twice from a goal down. We conceded while we were attacking.
"It was difficult, as they marked us in midfield, defended with eight men and went on rapid counter-attacks."