Liverpool manager Jurgen Klopp said his team's performance was "sensationally good" as Curtis Jones' stunning winner earned the Reds a fully deserved FA Cup third-round victory and extended Everton's miserable record of Anfield failure.
The German made nine changes from the side that increased their Premier League lead to 13 points with victory over Sheffield United on Thursday - including three debutants in Takumi Minamino, Nathaniel Phillips and substitute Yasser Larouci.
And it was 18-year-old Jones who grabbed the Merseyside derby glory with a magnificent curling 25-yard drive that eluded the outstretched arms of Everton keeper Jordan Pickford as it arced into the top corner after 71 minutes. The Toffees remain without a win at their rivals since September 1999.
Klopp said: "I saw a sensationally good performance of a not very experienced team with a lot of players playing for the first time on this kind of stage, in front of this crowd, against the opponent. It was outstanding. I loved it - I loved each second of this game.
"If you want to be a Liverpool player, you have to respect the principles of this club. We cannot always play the best football in the world but we can fight like nobody else. And as long as we use our principles, we will be a difficult opponent to play against."
The Reds boss had the luxury of resting superstars such as Sadio Mane, Mohamed Salah, Roberto Firmino and Virgil van Dijk, survived the early loss through injury of James Milner, and yet still saw his side fully merit their place in the fourth round.
Everton manager Carlo Ancelotti played virtually his strongest available side but the visitors paid for a lacklustre display and a succession of missed opportunities in the first half, when Dominic Calvert-Lewin, Mason Holgate and Richarlison saw efforts saved by Liverpool keeper Adrian.
The Italian blamed a drop in his side's performance level during the match.
"The line-up of Liverpool didn't affect our idea of how to play," he said. "We knew that Liverpool put in fresh players and that the intensity could be a high intensity, so I think the defeat arrived because we were not able to keep the intensity in the second half.
"We lost energy, we lost confidence, we were not able to build up quick from the back.
"We are going to speak and work together to find a solution to help improve the team. I know we have to work."
Liverpool are the team who have forgotten how to lose - and they were playing an Everton side who have long forgotten how to win at Anfield.
Klopp took no chances with his big players but the Reds still had too much energy for this laboured Everton team.
Divock Origi added physicality up front but it was the likes of Jones and 16-year-old Harvey Elliott who epitomised the host club's victory - along with 22-year-old central defender Nathaniel Phillips, effectively brought back from a loan spell at Stuttgart to play in this game.
It was a moment of genius from Jones, born two years after Everton last won at Anfield, that made the difference before Liverpool closed out the victory with maturity and without problems from a bitterly disappointing Everton.
They even survived the blow of losing Milner in the opening minutes, depriving Klopp of one of his most experienced players. In the event, it just gave another teenager, Yasser Larouci, his chance to shine.
Klopp and his players took the acclaim in front of the Kop after the final whistle as Liverpool's dream season continues.
Everton manager Carlo Ancelotti now knows the full extent of the job he must undertake at Goodison Park.