The Reds inflicted a first defeat of the season on the Serie A leaders as late goals from Mohamed Salah and Darwin Nunez sealed a 2-0 victory.
Advertisement
But it wasn't a big enough scoreline for the Merseyside outfit to leapfrog the Italian giants at the top of Group A with Liverpool forced to settle for second spot.
It looked to be a long night for the hosts at Anfield after Kvaratskhelia nutmegged Trent Alexander-Arnold after just 65 seconds.
Advertisement
Kvaratskhelia has been one of the standout players in Europe this season since joining Napoli from Georgian champions Dinamo Batumi in the summer.
He has chipped in with eight goals and ten assists from 17 games in all competitions to help Luciano Spalletti go five points clear at the top of Serie A.
But while he was unable to add to his goal contributions, he still put on a show with another dazzling display which left German gaffer Klopp purring.
Commenting on the Georgia international's battle with Alexander-Arnold after the match, Klopp said: "He is a good player, both are good players.
Advertisement
Advertisement
"It was a really difficult one. I know people will talk about one or two situations with Trent when he tried to get in front of him and the ball goes through.
"He is really good, the boy. Really quick, we have to defend it well together in these moments.
"When he has the advantage of the first moment, then he is already gone.
Advertisement
"You have to try to be there in the moment when the ball arrives. If you cannot to do that, you need to be protected because he has speed.
"He is cheeky, he can go inside, he goes outside, that always makes him difficult. A good player.
"Trent played a really good game against him, was really on fire.
Advertisement
"Didn't get frustrated by one or two situations where he was second-best. Stayed in the game. I liked Trent's game tonight."
It's not just Klopp who is a fan of Kvaratskhelia, with Manchester City claimed to be eyeing up a swoop to sign him following his explosive start to the campaign.
Meanwhile Real Madrid and Paris Saint-Germain are also said to be keeping tabs on him.
As a result of his stunning form, Napoli are alleged to already be looking to tie him down to a new contract - just months after he made the move to the Stadio Diego Armando Maradona.