Juventus had gone top before on Monday with a 4-0 win over Cagliari before Inter’s success set them back ahead.
Lukaku gave Inter the lead after a fine run from inside his very own half before he included a second with a shot that experienced goalkeeper Alex Meret’s legs.
Napoli’s Arkadiusz Milik scored from Jose Callejon’s low cross, yet Lautaro Martinez then got Inter’s third.
Lukaku has scored 14 Serie An objectives this season after his £74m move from Manchester United in August.
Just Lazio’s Ciro Immobile, with 19, has scored more class objectives in Italy in 2019-20 than the 26-year-old Belgian.
Cristiano Ronaldo is third in the goalscoring diagrams on 13 after he snatched his first Serie A cap stunt for Juventus in their basic home triumph.
Both Inter and Juventus are on 45 focuses from 18 matches, six clear of third-set Lazio while Napoli, who have lost two of their three matches since they sacked Carlo Ancelotti in December, are eighth.