Nicolo Barella scored with an excellent 20-yard strike to put Inter 1-0 lead when the Inter midfielder received the ball unmarked. He placed it nicely through the defenders at the right bottom corner.
The move for the second goal started with Lautaro Martinez, who set the ball for Ashley Young with a back-hill. Young kept that for Lukaku near the penalty spot. The Belgian turned a defender and slotted home for his 31st goal of the season.
Within three minutes of the second goal, Kai Havertz fired home from six yards to bring back Bayer into the match. With 66 minutes to go in the quarterfinal it was not looking impossible, given the game saw three goals in the first 24 minutes at either end.
Both the teams earned a qualification in European competition through their domestic league after a gruelling season this year. If Leverkusen had found a leveller that would have forced extra time in the one-off tie.
Despite an entertaining match, either of the teams failed to score further. Inter Milan had got two situations when Referee consulted VAR to rule out penalty-kick against Bundesliga side. Romelu Lukaku was all prepared to take the shot in both the occasions during the first half and injury time.
Milan based team will face the winner of Basel vs Shakhtar Donetsk in the semi-final in Dusseldorf.
Lukaku is the first player to ever score in nine UEFA Europa League matches in a row. However, this includes five games for Premier League side Everton in 2014-15.
The Serie A second-spot holder could have beaten Leverkusen by more if Lukaku, Eriksen, Sanchez and Moses were more clinical in their finishing effort.