The Rome club, riding high in second in Serie A, never looked in difficulty once Romanian defender Stefan Radu headed in a corner on the half hour.
Brazilian midfielder Hernanes converted Sergio Floccari's assist midway through the second half to seal matters before adding another classy goal in stoppage time.
Serie A leaders and defending champions Juventus host old rivals AC Milan in Wednesday's last-eight clash while Inter Milan welcome Bologna and Fiorentina play at home against Roma next week in the often unloved competition.
