Hopes of a comeback were dashed seven minutes from time when Sansone bagged his second, before Antonio Floro Flores added a fourth.
The hosts took the lead after 12 minutes when Zaza stroked home a left-footed volley from a Domenico Berardi corner to put Sassuolo one up.
It was not enough to earn a half-time lead, however, as the Serie B outfit hit back just after the half-hour mark through Coralli.
Berardi continued to menace after the restart and soon bagged his second assist, setting up Sansone as Eusebio Di Francesco's side moved ahead once more.
Cittadella pressed for an equaliser but they were undone on 83 minutes when Sansone secured his brace, while Flores struck a fourth goal in the dying moments to seal their progression.