The Viola handed starts to David Pizarro, Mati Fernandez, Cristian Llama and Mounir El Hamdaoui in a makeshift starting line-up.
Haris Seferovic nodded home the opening goal on 51 minutes before Ahmed El-Sayed Hegazi secured the victory with a second goal on 72nd minute after goalkeeper Andrea Seculin.
Murolo was sent off late on for the visiting side, but Fiorentina had already done enough to reach the fifth round.
There was also a 2-0 win for Siena over Torino courtesy of goals from Ze Eduardo and Reginaldo. Siena will play Lazio next at the Stadio Olimpico while Bologna joined with a 1-0 win over Livorno courtesy of a Cristian Pasquato goal.
Atalanta downed Cesena 3-1 with Reggina - 18th in Serie B - producing a shock 1- 0 at Serie A Chievo as Fabio Lucioni stunned the crowd at the Stadio Marc'Antonio Bentegodi with his 60th minute header.
Coppa Italia last 16 draw
Inter v Verona
Napoli v Bologna
Roma v Atalanta
Udinese v Fiorentina
Lazio v Siena
Parma v Catania/Cittadella
Milan v Reggina
Juventus v Cagliari/Pescara