Borja Mayoral scored twice to give Roma the win. Junior Moraes scored for Shakhtar which proved to be only a consolation goal with the tie ending 5-1 on aggregate. Roma will now look forward to the draw on Friday to see who they will face in the quarter-finals.
The match started with Shakhtar trying to take the initiative and press forward to try and begin to claw back the 3-0 deficit from the first leg.
Despite having good intentions, the home side struggled to create any meaningful chances in the first half. Roma understandably adopted a more patient approach, occasionally breaking forward on the counter.
Roma took the lead in the 48th minute through Borja Mayoral. The Spaniard placed his header into the corner of the net following some persistence from Rick Karsdorp down the right-hand side.
Shakhtar equalised when Junior Moraes was left unmarked at the back post and nodded home from close range.
Mayoral doubled his tally with twenty minutes to play, tapping in to finish off a superb passage of play involving Pedro and Carles Perez who sliced open the Shakhtar defence and left Mayoral with an open goal to grab his second.