Liverpool stretched their perfect Premier League start to maintain their stranglehold of the Merseyside derby with a 2-1 win over Everton and open up a six-point lead at the top of the table.
Goals from Ryan Gravenberch and Hugo Ekitike were the defending champions' reward for a dominant first half and enough for a fifth consecutive Premier League win.
But Liverpool ran out of steam after the break and were left hanging on after Idrissa Gana 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 their good work 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 ($135 million) plus signings Florian Wirtz and Alexander Isak on the bench, but Liverpool were all the better balanced for 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 unsurprisingly 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 to a fine team 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.
But the second half was a completely different story as Liverpool almost saw another two-goal lead disappear after being pegged by Bournemouth, Newcastle and Atletico already this season.
Fatigue this time seemed to play a part with kick-off just over 60 hours after Virgil van Dijk's stoppage time winner against Atletico on Wednesday.
Everton had a lifeline just before the hour mark when Grealish's deep cross was turned back into the path of Gueye, who blasted his past Alisson Becker.
Slot turned to Wirtz and Isak off the bench to try and wrestle back control to little effect.
Liverpool, though, did manage to see out a nervy finale to inflict an unwanted record on Everton boss David Moyes.
The Scot has now failed to win in 23 trips to Anfield as a visiting coach, the most any Premier League manager has played at a stadium without victory.