Inter Milan beat Bayer Leverkusen 2-1 and Manchester United scraped past FC Copenhagen 1-0, after extra time, to reach the Europa League semi-finals.
The Italians rode Lukaku's fantastic display to reach the next round. The forward helped force the opener for Nicolo Barella, then notched the second himself.
Kai Haverz pulled one back for Leverkusen, but Inter were on top and were twice awarded penalties, which were ruled out by VAR.
Lukaku added a third late on but it was harshly ruled out for a foul by the Belgian, which he did not appear to commit.
Ole Gunnar Solskjaer's Man United were below par in their win, which eventually was sealed when Bruno Fernandes scored yet another penalty, five minutes into extra time.
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Inter will face Shakhtar Donetsk or Basel, United will play Wolves or Sevilla.