Premier League champions Manchester City racked up a club-record 17th successive home win in all competitions but had to graft to a 1-0 victory over Newcastle United on Saturday.
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A superb strike from Julian Alvarez sealed the points for Pep Guardiola's side, but the relief they showed at the final whistle said a lot about a strong Newcastle display.
City's win lifted them to six points from two games alongside Brighton and Hove Albion who earlier in the day thumped Wolverhampton Wanderers 4-1 away.
Manchester United were unable to join City and Brighton at the top of the fledgling table though as they went down to a 2-0 defeat at Tottenham Hotspur in what was Ange Postecoglou's first home game in charge of the London club.
Liverpool came from a goal down to beat Bournemouth 3-1 although ended the game with 10 men after Alexis Mac Allister was shown a red card on his home debut.
Brentford are now unbeaten in 11 successive London derbies after they cruised to a 3-0 win at Fulham who also finished with 10 men after Tim Ream was sent off after conceding a penalty.
Manchester City made light of the absence of Kevin de Bruyne, who had surgery this week after damaging a hamstring in the 3-0 opening win over Burnley.
In their first home game since clinching the treble last season, City's stunning feat was honoured in grand fashion before kickoff at The Etihad Stadium.
City will be contending for multiple trophies again this season, but Newcastle showed why Guardiola has tipped them to be among the contenders for their Premier League crown.
That said, City were comfortably the better side in the opening half in which Alvarez broke the deadlock with a powerful strike in the 31st minute after being picked out by Phil Foden.
Newcastle grew in belief after the break but they discovered that for all City's attacking attributes, they also possess one of the tightest rearguards in Europe and Eddie Howe's side could find no way through to goal.
"There was a moment around 60-70 minutes in and I thought we could get control but they are a very good team and played through the press a few times," Howe said.
"They strangle you with the ball to a degree. You tire yourself out getting it back and with fatigue the decision making goes slightly."
Tottenham continued to banish the clouds of gloom that had preceded the new campaign as they proved there is life after Harry Kane with a vibrant display against a sloppy United.
Pape Matar Sarr's maiden Premier League goal, struck high into the net from a deflected cross just after halftime, and a late own goal by Lisandro Martinez sealed the victory which gave Tottenham four points from two games.
"We want to entertain for sure but in terms of being successful," Postecoglou said. "The atmosphere was incredible today. The energy the fans created was amazing."
Brighton's impressive start to the season continued and they are leading Man City on goal difference after crushing Wolves with three goals arriving in a devastating nine-minute spell in the second half against pointless Wolves.
Kaoru Mitoma opened the scoring for Brighton in the 15th minute with a sensational solo goal and he turned provider in the first minute of the second half to set up Pervis Estupinan.
Solly March then scored twice in four minutes, with Julio Enciso assisting him on both occasions.
Liverpool beat Bournemouth 9-0 a year ago but they found the south coast club a tougher nut to crack this time.
They went behind to an Antoine Semenyo goal but replied with goals from Luis Diaz, Mohamed Salah and Diogo Jota.
The gloss was taken off though as Mac Allister was sent off for a high tackle.
"Horrible start to the game," Liverpool manager Jurgen Klopp said. "We needed a few minutes to shake it off and then we were really good."
Bryan Mbeumo scored twice and Yoane Wissa was also on target as Brentford got the better of Fulham at Craven Cottage.
Fulham lost Ream when he conceded the penalty in the 63rd minute that allowed Brentford to go 2-0 up. "The game was finished from that moment," Fulham boss Marco Silva said.
West Ham United face Chelsea on Sunday with Aston Villa at home to Everton – all four sides seeking a first win.