Luis Diaz salvaged a 1-1 draw for Liverpool against Crystal Palace at Anfield despite Darwin Nunez having been sensationally sent off for a headbutt on his full debut.
Thomas Tuchel and Antonio Conte were both sent off as tempers flared after Harry Kane's last-gasp equaliser earned Spurs an unlikely 2-2 draw at Chelsea.
Manchester United put in one of their worst Premier League performances in 30 years as they were thrashed 4-0 by Brentford.
Graham Potter praised the "excitement and intent" of his Brighton side but admitted he "couldn't believe we didn't score" past Newcastle's inspired Nick Pope.
Southampton came from two goals down to rescue a point in a 2-2 draw with Leeds, ending a run of five consecutive PL defeats.
Man City sent out an ominous warning to the rest of the Premier League after brushing aside Bournemouth 4-0 despite Erling Haaland failing to score.
Aleksandar Mitrovic missed a late penalty for Fulham as Wolves goalkeeper Jose Sa saved his spot-kick to ensure it finished goalless at Molineux.
Gabriel Jesus was red hot as he struck his first two competitive goals for Arsenal in a dramatic 4-2 win over Leicester on a sweltering afternoon at Emirates Stadium.
Goals from Danny Ings and Emiliano Buendia secured a 2-1 win for Aston Villa over Everton as Steven Gerrard got the better of Frank Lampard at Villa Park.
Substitute Karlan Grant headed West Brom into the Carabao Cup second round as they edged Sheffield United 1-0 at The Hawthorns.
David Alaba and Karim Benzema scored in each half as Real Madrid beat Eintracht Frankfurt 2-0 in Finland to win the UEFA Super Cup for a record-equalling fifth time.
Rangers produced an impressive comeback to beat Union Saint-Gilloise 3-2 on aggregate in their Champions League qualifier and book their place in the play-off round.
Manchester City began their Premier League title defence in confident fashion by brushing aside West Ham 2-0 in front of a record crowd at the London Stadium.
Pascal Gross' first-half double gave Brighton a 2-1 win at Man Utd as Erik ten Hag's reign got off to the worst possible start.
Brentford boss Thomas Frank hailed his side's determination and mentality after the Bees fought back from two goals down to snatch a deserved 2-2 draw at Leicester.
Borussia Dortmund beat Bayer Leverkusen 1-0 in their Bundesliga opener on Saturday but their winning start was overshadowed by an injury to new signing Karim Adeyemi.
Jesse Marsch's new-look Leeds got off to the perfect start as they came from behind to beat Wolves 2-1 at Elland Road.
Tottenham began their new Premier League season with a comfortable 4-1 home win over Southampton, despite the visitors taking a surprise lead.
Superb goals from Fabian Schar and Callum Wilson saw Newcastle ease past Nottingham Forest 2-0, but Eddie Howe wants his side to be more ruthless in front of goal.