Roma reach Italian Cup quarters
The home side rested a number of first teamers including recent loan signing Luca Toni but still prevailed easily.
Triestina striker Luigi Della Rocca gave them an early shock with a fifth minute goal but Matteo Brighi equalised on the stroke of half-time.
Forwards Mirko Vucinic and Julio Baptista sealed victory in the second half.
Serie A leaders Inter Milan progressed from the last 16 in December with a 1-0 win over Livorno while AC Milan host third tier Novara on Wednesday and troubled Juventus play Napoli.