Manchester United's new-manager bounce fell flat as they shared the points in a stale 1-1 draw with Chelsea at Old Trafford.
Dominic Solanke scored twice as Tottenham roared back from a goal down to thrash top-four rivals Aston Villa 4-1 at the Tottenham Hotspur Stadium.
Chris Wood continued his fine form in front of goal after netting the opener against West Ham United during a 3-0 win which took Nottingham Forest into third.
A quickfire double from Gakpo and Salah sees Liverpool come from behind to beat Brighton 2-1 at Anfield to move top of the league.
Jordan Ayew came off the bench to earn Leicester a last-gasp 1-1 draw at Ipswich as Kieran McKenna's side's wait for a first league win of the season continues.
Arsenal slipped further off the pace at the top of the Premier League table after Alexander Isak's brilliant early header handed them a 1-0 defeat at Newcastle.
Cole Palmer produced "one of the best passes in Premier League history" to help Chelsea overcome Newcastle United 2-1 at Stamford Bridge.
Robert Lewandowski scored twice with Lamine Yamal and Raphinha also netting as Barcelona thrashed Real Madrid 4-0 at the Santiago Bernabeu.
Evanilson's header in the last seconds of stoppage time stunned Aston Villa and earned Bournemouth a 1-1 draw at Villa Park.
Wolves came back from being 2-0 down in the 85th minute to snatch a point at Brighton after Matheus Cunha scored a dramatic added-time equaliser.
Erling Haaland struck a first-half winner as Manchester City moved to the top of the Premier League with a 1-0 victory over Southampton.
Bryan Mbeumo scored a stoppage-time winner to maintain Brentford's unbeaten home run against winless Ipswich, who took a two-goal lead in the first half.
Chris Wood continued his red-hot scoring form with a second-half double that sent Forest fifth in the Premier League after a 3-1 win at East Midlands rivals Leicester.
Fenerbahce boss Jose Mourinho was sent off as Man Utd held on for a 1-1 draw in Istanbul in the Europa League.
A late Mohamed Salah equaliser rescued a 2-2 draw for Liverpool at absence-hit Arsenal to move them a point off the top of the table.
Crystal Palace claimed their first win of the Premier League season as Jean-Philippe Mateta's first-half strike sealed a 1-0 victory over Tottenham.
Jarrod Bowen scored a controversial 90th-minute penalty as West Ham grabbed a 2-1 win over wasteful Man Utd to leapfrog Erik ten Hag's side in the table.
Beto's stoppage-time equaliser extended Everton's unbeaten run to five matches to secure a 1-1 draw and deny Fulham a fourth straight victory at Goodison Park.
Chris Wood heaped more misery on blunt Crystal Palace with the decisive goal in a scrappy 1-0 victory at the City Ground.
The Football Association has asked Gary O’Neil for his observations on his post-match comments about the refereeing of Wolves’ 2-1 defeat to Manchester City.