Arsenal maintained their perfect start to the Premier League season with a fifth consecutive win but Manchester City's new signing Erling Haaland stole the limelight with his second hat-trick in 6-0 romp over Nottingham Forest on Wednesday.
Newcastle United's record signing Alexander Isak scored on his debut to put his side ahead at Anfield but Liverpool snatched a 2-1 victory deep in stoppage time through Fabio Carvalho.
Tottenham Hotspur remained unbeaten but were held to a 1-1 draw at West Ham United.
Haaland's eagerly-awaited arrival at Manchester City has seen the Norwegian make a spectacular impact.
After scoring three times in the second half in a win over Crystal Palace at the weekend, Haaland struck three times in the opening 38 minutes as rampant City overwhelmed Forest.
He has scored nine goals in five league games since joining City from Borussia Dortmund -- a record.
"It was about keeping doing what we did in the second half against Palace, play, play, play -- it was nice. It's been good so far, I'm not complaining," he said.
Haaland put City ahead in the 12th minute after a pass by Phil Foden and Foden provided the assist for Haaland's second.
Haaland completed his treble with a powerful header.
Argentine Julian Alvarez, another new signing for the champions, scored twice after the break as City again displayed their formidable firepower.
City have 13 points from their five games and have scored 19 goals but Arsenal are setting the pace.
Mikel Arteta's claimed a fifth win as they edged Aston Villa 2-1 at The Emirates -- Brazilian strike duo Gabriel Jesus and Gabriel Martinelli both on target for the Gunners.
Jesus opened the scoring in the 31st minute and Martinelli grabbed the 77th-minute winner, three minutes after struggling Villa had equalised when substitute Douglas Luiz scored directly from a corner.
"We are really happy because we are winning football matches the way we deserve," Arteta said. "We need to improve and you could see that in the second half, but the way we played in the first half is really pleasing as a coach."
The 22-year-old had a goal disallowed in the second half as Liverpool were rocking.
Liverpool finally woke up and struck back in the 61st minute when Roberto Firmino drove home Mohamed Salah's cut-back.
Newcastle defended desperately for a point but were left crestfallen when Carvalho thumped home the winner in the eighth minute of stoppage time to move up to fifth in the table on eight points, with Newcastle 11th on six.
"Football can go in both directions but tonight it went in the right one, a perfect end of the game," said Liverpool manager Juergen Klopp, who accused Newcastle of time-wasting.
His opposite number Eddie Howe was less happy.
"I am really proud of the players, proud of the commitment but that is very painful," he said.
Tottenham, who could have joined Manchester City on 13 points, led at West Ham thanks to an own goal by Thilo Kehrer.
But Tomas Soucek earned West Ham a deserved point with a 55th-minute leveller.
Bournemouth, who sacked manager Scott Parker this week in after their 9-0 hammering at Liverpool, regrouped with a 0-0 draw at home to Wolverhampton Wanderers.