Belgian Lukaku related with Nicolo Barella’s cross within the 119th minute to Fiorentina goalkeeper Pietro Terracciano and snatch a late triumph.
Chilean Arturo Vidal had given Inter the benefit 5 minutes earlier than the break in regular time after a VAR assessment judged Terracciano to have fouled Alexis Sanchez.
However Christian Kouame blasted in an excellent equaliser 12 minutes after half-time to take the match to extra-time.
Lukaku got here off the bench on 69 minutes and ensured Inter averted going to a penalty shootout along with his 17th purpose this season in all competitions.
AC Milan received 5-Four on penalities on Tuesday after their match towards Torino ended Zero-Zero after further time.
Title-holders Napoli are at residence towards Empoli later Wednesday with document 13-time winners Juventus taking up Genoa in Turin.