Inter manager Antonio Conte showed the same faith with the eleven that did the business over LaLiga outfit Getafe last Tuesday evening.
The Italian side drew first blood with 15 minutes played after Nicolo Barella latched onto Romelu Lukaku's blocked shot before nestling home from outside the box.
Inter had a second right after the 20-minute mark when Lukaku held his own against Edmond Tapsoba to find the back of the net following good thinking by Ashley Young.
Leverkusen hit back four minutes later when questionable goalkeeping from Samir Handanovic helped Kai Havertz's rasping shot to arrow into the roof of the net.
The Nerazzurri were awarded a penalty after Danilo D'ambrosio's cross contracted Daley Sinkgraven's shoulder, but it was overturned by the Video Assistant Referee in the 28th minute.
Roberto Gagliardini went inches close to giving Inter a third from a corner delivered by Young, but he couldn't take advantage-bringing an exciting half to conclusion.
Leverkusen were on the mend following halftime, with Diego Godin needed to make a timeous challenge from Kevin Volland's probing aim at Handanovic's goal.
The Bundesliga side upped the ante with Leon Bailey entering for Exequiel Palacios just before the 60th minute as the search to go level intensified.
Inter were hell-bent not to surrender their advantage two minutes later, as Christian Eriksen brought Lukas Hradecky to a smart and low save.
The Milan-based side looked to have been given another penalty deep in added time after a foul on Eriksen, but VAR once more disapproved though the side still progressed to the last four.