Lukaku, the talented Belgian striker, made a significant impact in his debut season with the 2023 Italian champions by scoring his fourth goal of the campaign. He demonstrated his goal-scoring prowess by breaking the deadlock just five minutes into the match.
He raced onto a pass from Frank Anguissa, held off a defender and slotted coolly past Mike Maignan in the AC Milan goal.
Napoli goalkeeper Alex Meret was forced twice into action before the half-hour to maintain his side's lead.
As the clock ticked down to half-time, Georgian winger Kvaratskhelia doubled the visitors' lead.
Picking the ball up on the left wing, he drove suddenly inside on his right foot past Youssouf Fofana and rifled a shot from distance into the far post beyond the dive of Maignan.
Alvaro Morata thought he had given Milan a lifeline two minutes after the break with a powerful header.
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However, upon VAR review he was shown to have been offside in the build-up to the goal and it was disallowed.
The hosts continued to search for a way back into the encounter and only a fine reflex save by Meret to deny Rafael Leao in the 83rd minute kept Napoli's two-goal cushion intact.
Earlier, goals in either half by Riccardo Orsolini and Jens Odgaard sent Bologna up to 10th in the table with a 2-0 win at Cagliari.
Lecce climbed off the foot of the table by beating nine-men Verona 1-0 thanks to a Patrick Dorgu goal on 51 minutes.
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The away side lost Jackson Tchatchoua to a red card five minutes before half-time, then Reda Belahyane was given his marching orders inside the final 10 minutes for a second bookable offence.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)