In a frantic fixture from start to finish, first-half goals from Nicolo Barella, Lukaku and Kai Havertz set the tone of the match, before Inter held out to make their first European semi-final since 2010 - where they went on to win the Champions League.
There was no space for either Christian Eriksen or Alexis Sanchez in an unchanged Inter side, while Chelsea target Kai Havertz started for Leverkusen after being described as the club's all-time best player by manager Peter Bosz, who made two changes to the side that saw off Rangers last week.
In what was Inter's first European quarter-final since 2011, it was the Italian side who took the lead as Nicolo Barella found the bottom corner with the outside of his boot after Lukaku's initial shot was cleared.
Inter's lead was doubled after just 20 minutes as Lukaku set a new record by scoring in his ninth consecutive Europa League game. He was simply too strong as he received Ashley Young's ball in the box, before turning and squeezing under Lukas Hradecky despite being pulled to the floor.
Leverkusen - who have scored in every game in 2020 - hit back just two minutes later as Havertz slotted through the legs of Samir Handanovic to grab his 18th goal of the season.
A non-stop first half showed no signs of slowing down there, as Inter were almost immediately awarded a penalty after Daley Sinkgraven was adjudged to have handled in the area, before the referee - with the use of the pitch-side monitor - overturned his decision.
The second half continued in blistering fashion, and after coming on as substitutes, Eriksen and Sanchez combined for what would have been a sublime goal. The former Tottenham man fooled everyone as his perfectly disguised pass found the Chilean, whose volleyed effort was well saved.
In holding on for victory, an under-pressure Antonio Conte survives to live another day. His side will face the winner of Shakhtar Donetsk or Basel - who play tomorrow - for a place in the final.
As for Leverkusen their season has now come to an end; and that was perhaps the last game Havertz will play for the German club, who have been adamant he would see out their Europa League campaign.
Inter were awarded a penalty once more on the stoke of added time as Eriksen was dragged down in the box. Again, taking to the pitchside monitor, the referee overturned the penalty for a Barella hand ball in the build up.
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