Kvaratskhelia scored just before half-time
Napoli moved seven points clear at the top of Serie A with a clinical 2-0 win at AC Milan.
Former Inter Milan forward Romelu Lukaku made an instant impact on his return to the San Siro, opening the scoring after five minutes as he outmuscled Strahinja Pavlovic inside the penalty area before firing into the bottom corner.
Despite a response from Milan, who tested Napoli goalkeeper Alex Meret on a handful of occasions, Khvicha Kvaratskhelia doubled the lead for the visitors minutes before half-time.
The Georgia international embarked on one of his trademark mazy runs down the left wing, chopping past several defenders before unleashing a curling drive beyond the hands of Mike Maignan.
Immediately after the restart the hosts looked to have halved the deficit through Alvaro Morata but his header was ruled out for a marginal offside.
Victory takes Antonio Conte's side to 25 points, seven clear of Inter Milan in second.
A third defeat of the season leaves AC Milan in eighth place, 11 points off the pace.
From 'melting like snow' to solid as ice
Antonio Conte has already won Serie A on four occasions, three times with Juventus and once with Inter Milan
After an embarrassing 3-0 opening day defeat away to Verona in his first game in charge, Conte said that his Napoli side had "melted like snow in the sun".
Many a Napoli fan may have feared that their side were set to carry over their poor form from the 2023-24 campaign in which, as reigning champions, they finished 39 points off the top.
But the turnaround since matchday one has been remarkable.
Conte’s side are now unbeaten in nine games, winning eight and drawing one, scoring 18 goals and conceding just two. They only dropped points once in that run: a 0-0 draw away to Juventus in mid-September.
That was one of eight clean sheets in 10 games this season, with the latest on Tuesday night built on five saves from goalkeeper Meret and several blocks from centre-halves Amir Rrahmani and Alessandro Buongiorno.
Four-time Serie A winner Conte has brought his signature steeliness and nous to Naples.
Having "melted" on matchday one, Napoli now look as solid as ice, an impermeable winning force who look set to challenge for the title once again.
