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United thrashed Leeds 5-1 in Saturday's lunchtime kick-off, courtesy of a hat-trick from their Portuguese talisman Bruno Fernandes, before European champions Chelsea crushed Patrick Vieira's Crystal Palace 3-0 at Stamford Bridge.
In the day's late game, man-of-the-match Mohamed Salah claimed assists on goals for Diogo Jota and substitute Roberto Firmino, before scoring one of his own to help Liverpool to a comprehensive 3-0 win at newly-promoted Norwich.
The return of near-capacity crowds fuelled a barrage of goals - and a bunch of home wins - on the first Saturday of the season, with Manchester United manager Ole Gunnar Solskjaer reckoning it was "a perfect day" for 72,000 spectators - Britain's biggest football crowd since the pandemic - at Old Trafford.
Fernandes scored his treble after new signing Raphael Varane had been paraded in front of the Stretford End.
Paul Pogba also starred for United with four assists - one more than he managed in the whole of last season in the league - as United ran riot with other goals from Mason Greenwood and Fred.
United's win was the highest-scoring encounter on a day featuring 25 goals across seven matches. That's 3.57 per game, which is much higher than a typical season's average.
The presence of fans may also have contributed to there being five home wins, an immediate swing from last season when there were more away wins (40% compared to 38% for home teams).
Everton rallied from a goal down to beat Southampton 3-1 as manager Rafa Benitez enjoyed a winning start to his reign at Goodison Park while Jamie Vardy scored a brilliant winner in Leicester's 1-0 victory over Wolves.
Emmanuel Dennis and Cucho Hernandez scored on their debuts as Watford made a winning return to the top-flight by beating Aston Villa 3-2 and Brighton's Neal Maupay and Alexis MacAllister scored superb second-half goals to seal a 2-1 victory at wasteful Burnley.
Chelsea, fresh from their UEFA Super Cup win in midweek, were dominant against Palace, defenders Marcos Alonso and Trevoh Chalobah - with his first goal for Chelsea, on his Premier League debut - scoring either side of a close-range strike by US forward Christian Pulisic.
Palace look set for a tough year under Vieira, the former Arsenal and France star who has replaced Roy Hodgson in his first senior managerial role in English soccer.
With defensive lynchpin Virgil van Dijk back after nine months out with a serious knee injury, Liverpool enjoyed a relatively trouble-free evening at Carrow Road, manager Jurgen Klopp saying it was "pretty much as good as it gets".
Norwich had their chances but once Jota gave Liverpool the lead in the 26th minute the visitors were in command.
Salah set up Firmino to make it 2-0 in the 65th minute and then sealed the points nine minutes later with a neat finish - the fifth straight season he has netted in the first round of matches.
"Each game helps and it was really good to see Virgil again on the pitch, especially on defensive set-pieces," Klopp added.