Romelu Lukaku scored after just 21 seconds as he bagged a brace in a 4-1 thumping of Cagliari that fired Inter Milan into the last eight of the Italian Cup, while Lazio and Napoli are set for a quarter-final clash after easing past second-tier opposition.

Belgian Lukaku has looked like a player reborn since moving to Italy and his double took his hot streak to six goals in his last four appearances in all competitions, with his Serie A tally standing at 14 in 19 games.

"Inter was the best choice for me, here I can grow as a player and help the club go after its goals," Lukaku told broadcaster RAI.

"I give everything for the team and that's how I play – that's what the fans like."

The 26-year-old lashed home his opener with the match barely underway and then, after Borja Valero had made it 2-0 in the 22 minute, headed home his side's third from Nicolo Barella's corner just three minutes after the break as Antonio Conte's side ran riot at the San Siro.

Their were nerves among the home fans when Christian Oliva pulled one back for the Sardinians in the 73rd minute with a fierce drive, but Andrea Ranocchia headed in Cristiano Biraghi's corner to seal the win.

The victory helped Inter bounce back after letting Juventus the take top spot in Serie A with a 1-1 home draw with Atalanta at the weekend, and the return of Alexis Sanchez after an injury lay-off will also boost coach Conte.

Inter will face either Atalanta or Fiorentina, who face off on Wednesday afternoon, in the next round.

They will be joined in the quarters by Lazio and Napoli, who both cruised through with comfortable wins over second-tier sides Cremonese and Perugia to set up a mouth-watering last eight tie with each other.

Elsewhere, Tottenham edged into the FA Cup fourth round as Giovani Lo Celso bagged a rare goal in their 2-1 win over Middlesbrough, while much-maligned Newcastle striker Joelinton scored for the first time since August in a victory against Rochdale on Tuesday.

Jose Mourinho's side almost killed off second-tier Middlesbrough within the first 15 minutes of the third round replay at the Tottenham Hotspur Stadium.

Lo Celso, on loan from Real Betis, got Tottenham up and running with only his second goal of the season and his first since a Champions League strike against Red Star Belgrade in November.

It was an encouraging moment for the Argentine midfielder, who has endured a difficult season in north London.

Tottenham needed a Lucas Moura equalizer at the Riverside Stadium to avoid a shock exit in the 1-1 draw at Middlesbrough earlier this month.

But Mourinho still made five changes from last weekend's defeat against Liverpool, with Christian Eriksen, linked with a January move to Inter Milan, starting despite the Dane's form being affected by the transfer talk.

A gift from Middlesbrough keeper Tomas Mejias helped Tottenham open the scoring in the second minute.

Mejias tried to play a quick ball out and ended up passing straight to Lo Celso, who ran across the area before firing into the bottom corner.

Tottenham's second came when Argentina winger Erik Lamela sliced through the Middlesbrough defence before slotting home in the 15th minute.

George Saville got one back for Middlesbrough in the 83rd minute as Tottenham survived a tense finale to earn a trip to Southampton.