Jose Mourinho’s side, trailing 1-0 from the first leg, took the lead after an hour through Leonardo Spinazzola.
Stephan El Shaarawy and Lorenzo Pellegrini then made it 4-1 on the night as Roma won 4-2 on aggregate.
Roma also beat Feyenoord last season in the final of the Europa Conference League.
They face Bayer Leverkusen in the semi-finals after the German side comfortably beat Union Saint-Gilloise 4-1 in their second leg to win 5-2 on aggregate.