Early Federico Dimarco’s goal separated both sides after an initial 1-1, as it proved enough for Inter to eliminate Juventus from the competition.
The win, therefore, gives Inter Milan Italia a chance to retain its trophy.
The game would have ended in penalties if no goals had no away goals rule.
Inter will now face either Fiorentina or Cremonese on May 24.
Lukaku returned after Ben handed a red card in the tie ended in chaos, but the Belgian was pardoned because his gesture silencing the crowd was aimed at racist fans.
Inter were in front gear within the first five minutes as an unmarked Lautaro Martinez grazed his head to a Nicolò Barella ball flashed across the six-yard box.
Alex Sandro made a huge clearance when he prevented Denzel Dumfries from nodding in at the back post from a corner flicked on by Alessandro Bastoni.
A few minutes later, Inter took the lead on their third attempt. This time, Barella released a through ball off the outside of the boot, perhaps meant for Edin Dzeko, but instead, found Federico Dimarco to scuff into the far bottom corner from 12 yards.
As Inter continued to push for another game, Andre Onana was called into action as he made his first save in 34 minutes. The Cameroonian used his gloves to stop a sudden long-range Filip Kostic strike.
With no attacking threat from Juventus, Max Allegri introduced Arkadiusz Milik while Locatelli drilled straight at Onana.
Edin Dzeko thought he had made it 2-0, but the goal didn’t stand as he was offside.
Both goalies were in action to make some saves as the scoreline stayed till the end of regulation time for Inter to secure the finals ticket.
This is expected.be a huge boost for Simone Inzaghi’s men after their difficult form leaves them 6th 9n the Serie A table with eight games to go.