Sevilla's win, in a tie reduced to a single match played in Duisberg, Germany, after the first leg was called off at the start of the COVID-19 outbreak, earned them a meeting with Olympiakos or Wolverhampton Wanderers on Tuesday.
Roma, who finished fifth in Serie A after winning seven of their last eight games, appeared to be coming back into the match when Sevilla struck again.
The La Liga side broke up a Roma attack, Lucas Ocampos was set free down the right and pulled the ball back for En-Nesyri to turn into an empty net shortly before halftime. Roma had Gianluca Mancini sent off in stoppage time.
The last eight will be played in four German cities as part of the mini-tournament, with the final on Aug. 21 in Cologne.