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Consecutive draws had seen the Nerazzurri pass up the opportunity to capitalise on Juventus' shaky form, with the leader still able to seal the Scudetto against Sampdoria on Monday (AEST).

But even with its title hopes virtually extinguished, Antonio Conte's side was back on its game at Luigi Ferraris to move up to second.

Lukaku nodded in his 22nd league goal of the season 34 minutes in and, after Alexis Sanchez added a late second, got his 23rd with a marvellous individual effort, leaving Genoa still just four points clear of the bottom three, having played a game more than 18th-placed Lecce.

Pressure had steadily built on the Genoa goal after a slow Inter start, with Lukaku – at the heart of all of their best work – helping to create chances for Marcelo Brozovic and Christian Eriksen, both of which were squandered.

The Belgium striker made sure the visitors were in front heading into half-time as he ghosted into the area to meet Cristiano Biraghi's searching cross with a firm header in off the post.

A curling Filip Jagiello free-kick provided a brief scare, yet a low-key second period saw few clear openings at either end.

Although Genoa belatedly threw men forward in search of an equaliser, it was swiftly caught out in defence at the other end and substitute Sanchez netted via the bar after fine work from Victor Moses on the right.

There was still time for Lukaku to produce the moment of the match, racing forward deep into stoppage-time and cutting inside past desperate challenges to hammer in the third.

The fixture list does not make easy reading for Inter, even if its league season is essentially over. It faces Napoli next, followed by Atalanta and Getafe. Genoa does still need points and visits Sassuolo on Thursday (AEST).