Romelu Lukaku headed in an extra-time winner as Inter Milan set up an Italian Cup quarter-final clash with city rivals AC Milan on Wednesday with a 2-1 last-16 win over Fiorentina.

Belgian Lukaku connected with Nicolo Barella's cross in the 119th minute to beat 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 with a minute to go ensured Inter avoided going to a penalty shootout with his 17th goal this season in all competitions.

"It was an important win for our confidence against a strong team," said Lukaku days before Inter host champions Juventus in Serie A.

"We are a young team, we need to learn, but we're growing and we have shown the desire to improve."

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.