Mohamed Salah scored twice as Liverpool beat Arsenal 3-1 to open up a three-point lead at the top of the Premier League.
Joel Matip headed Liverpool in front four minutes before the break, rewarding their first-half superiority from a Trent Alexander-Arnold corner.
Liverpool doubled their lead four minutes after the restart when David Luiz grabbed Salah's shirt following a delicious touch from Roberto Firmino.
Salah swept home from the penalty spot and secured Liverpool's third straight victory after 58 minutes.
The Egyptian left Luiz trailing in his wake before bursting into the area and finishing unerringly.
Arsenal's 100 per cent record was well and truly gone, but substitute Lucas Torreira struck a consolation five minutes from time to give the Gunners some cheer.
Liverpool are now the only Premier League side with a 100 per cent record this season and extended their winning run to 12 league matches.
Jurgen Klopp felt this performance represented a step up, saying: "I was really happy with a lot of parts of the game. I think everything we did well in the first four games we did tonight longer, more precise and better attuned.
"And I loved the desire, the passion, the power, the energy we put into this game that made us really uncomfortable to play against. We have a lot to improve but it was a big step tonight and I'm really happy."
Arsenal look to have recruited well and returning to the top four should be their target for the season but, on this showing, anything more looks unlikely. Anfield has been a venue of horrors for the Gunners in recent seasons and they were completely outplayed again here.
Sadio Mane has been the main man for goals for Liverpool so far this season but here Salah stole the show. His penalty was struck with supreme confidence while his second goal was the best of the Egyptian, running past defenders and never looking for a moment like he was about to miss.
Adrian may have been the Super Cup hero but Liverpool fans will be counting down the days until Alisson Becker is fit again. After presenting Southampton with a goal last weekend, the Spaniard was shaky here in his handling and kicking and was fortunate not to cost his team again.
Arsenal gave club record signing Nicolas Pepe his full debut and it was impossible to miss the 24-year-old in his shocking pink boots. He caught the eye with his skill, too, giving Virgil Van Dijk one of his more uncomfortable afternoons despite Liverpool's dominance. All that was missing from Pepe was precision in front of goal. He was prolific at Lille so Arsenal will hope that will come.
Chelsea fans knew to expect a mixed bag from Luiz and, if this display is anything to go by, the same will be true for Arsenal supporters. He was one of the best players on the pitch in the first half, repelling attack after attack, but a blatant pull on Salah's shirt gave away a penalty and he was then comprehensively beaten by the Egyptian for the third.