Lukaku books Inter Italian Cup quarter-final clash with AC Milan
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Belgian Lukaku connected with Nicolo Barella's cross in the 119th minute to Fiorentina goalkeeper Pietro Terracciano and snatch a late triumph.
Chilean Arturo Vidal had given Inter the advantage five minutes before the break in normal time after a VAR review judged Terracciano to have fouled Alexis Sanchez.
But Christian Kouame blasted in a superb equaliser 12 minutes after half-time to take the match to extra-time.
Lukaku came off the bench on 69 minutes and ensured Inter avoided going to a penalty shootout with his 17th goal this season in all competitions.
AC Milan won 5-4 on penalities on Tuesday after their match against Torino ended 0-0 after extra time.
Title-holders Napoli are at home against Empoli later Wednesday with record 13-time winners Juventus taking on Genoa in Turin.