Three-time former winners Inter struck first through Nicolo Barella as he guided in from the edge of the area on 15 minutes, with Lukaku bundling in a second six minutes later.
Kai Havertz reduced the deficit in possibly his final game for Leverkusen with a well-worked goal on 25 minutes after exchanging passes with fellow Germany international Kevin Volland, but Inter held on to seal their place in the semi-finals.
Antonio Conte’s side will take on Ukrainian champions Shakhtar Donetsk or Swiss club Basel next Monday in Dusseldorf for a place in the final on August 21.
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