Liverpool extended their perfect Premier League start and maintained their stranglehold of the Merseyside derby with a 2-1 win over Everton that opened up a six-point lead at the top of the table.
Goals from Ryan Gravenberch and Hugo Ekitike were enough for the defending champions' fifth consecutive Premier League win.
Liverpool have now won five consecutive home games against the Blues for the first time since 1933-37.
Everton manager David Moyes thus remained winless in 23 games at Anfield with the Toffees, Manchester United, Sunderland and West Ham.
However, Liverpool ran out of steam after the break and were left hanging on after Idrissa Gueye fired Everton back into the contest.
Arne Slot's men had needed late goals to win all of their previous four Premier League games and Champions League opener against Atletico Madrid in midweek.
This time, the Reds did the bulk of the heavy lifting inside the first 30 minutes to leave Everton still without a win at Anfield in front of a crowd in the 21st century.
Slot left both his £100 million plus signings Florian Wirtz and Alexander Isak on the bench, but Liverpool looked better balanced upon the return of Alexis MacAllister alongside Dominik Szoboszlai and the impressive Gravenberch in midfield.
The Dutch midfielder broke the deadlock just nine minutes in with a deft finish on the half-volley from Mohamed Salah's cross.
Salah came close to a second moments later with a powerfully struck effort on his trusty left foot that flew just wide.
Everton had been on a four-game unbeaten run thanks in large part to the form of the resurgent Jack Grealish.
The Manchester City loanee was again at the heart of their best first-half move with a pass through to Kieran Dewsbury-Hall who fired wide from a narrow angle.
Liverpool responded in style when a fine move culminated in Ekitike rolling Gravenberch's pass through the legs of Jordan Pickford for his third goal in five Premier League games since his move from Eintracht Frankfurt.
The second half was a different story as Liverpool almost saw another two-goal lead disappear after being pegged by Bournemouth, Newcastle and Atletico already this season.
While Slot was preparing his first changes – Curtis Jones and Wirtz – to re-energise his side, Grealish swung a cross to the far post where Iliman Ndiaye laid it back for Gueye to smash home.
Isak replaced Ekitike not long after but even the British record signing, still short of match fitness, struggled to turn the tide back in Liverpool's favour.
The full-time whistle came as something of a relief for the hosts, who extended their current narrative of winning while being far from their best.
Everton's season, meanwhile, has stalled after the international break but Moyes will take encouragement from their second half even if it did not amount to anything.
Grealish, speaking to TNT Sports, said: “It was what I expected. I don't think we played well in the first-half, we came in a half-time and had a chat with the manager and then second half, we lost the game in the second half.
“Frustrating because if we had played like that, pressed like that from the start it would have been a different game. In the end we couldn't get that last goal.”
