Arsenal beat Tottenham 3-1 in the north London derby, while Manchester City ended Chelsea's unbeaten start in the Premier League with a 1-0 victory at Stamford Bridge.
Leaders Liverpool were held in a thrilling 3-3 draw with Brentford, while Manchester United were beaten 1-0 at home by Aston Villa.
Meanwhile, Burnley, Newcastle, Leeds, Norwich and Southampton all remain winless after six matches.
Leicester denied Burnley with a late equaliser in a 2-2 draw and Newcastle drew 1-1 with Watford.
Everton beat Norwich 2-0, Leeds lost 2-1 at home to West Ham and Southampton lost 1-0 to Wolves.
Check out my team of the week and then make your own selections towards the bottom of the article.
Goalkeeper: Emiliano Martinez (Aston Villa)
When Arsenal let this goalkeeper slip through their fingers and go to Aston Villa I thought they had made a terrible mistake. I thought it then and I still think it now.
Villa on the other hand have benefited tremendously from his outstanding performances. Against Manchester United the Argentine was at his best.
I watched in amazement when United were awarded a penalty to see Martinez challenge Cristiano Ronaldo to a duel, daring him, almost taunting him to take the penalty. Fernandes is United's official penalty taker and missed the spot-kick but the sheer audacity, not to mention the confidence, of Martinez impressed the hell out of me.
Did you know? Manchester United attempted a total of 28 shots at Martinez's goal without scoring. That's the most they have attempted in a home Premier League game without finding the net since October 2016.
Defenders: Aymeric Laporte (Manchester City), Kortney Hause (Aston Villa), Ruben Dias (Manchester City)
Laporte: This was a very impressive defensive display by Manchester City. I've often thought you can cause City problems, especially on the counter-attack, but the combination of Aymeric Laporte and Ruben Dias looked quite impregnable against Chelsea.
I know both players are comfortable on the ball but I have never been totally convinced about either player's ability to cope with the physical aspects of the Premier League.
Well if anyone is going to test your commitment to a football match then it's going to be Romelu Lukaku. The Chelsea striker put them both to the test and got very little out of either.
Did you know? Manchester City have conceded one goal in their six league games this term - the fewest at this stage of a league season in their history.
Hause: What a header. The ball was great but the movement by Hause, not to mention the finish, was sensational. If you insist on not putting a player on the near post when defending corners in the modern game then make sure you win your headers.
Manchester United did neither against an Aston Villa side who look like they are coming to terms with the departure of Jack Grealish.
I thought the penalty awarded against Hause for handball was harsh but that was the opinion of the referee Mike Dean. He's not my favourite referee but it was at least his decision and not VAR's. As for Solskjaer whinging about an infringement by Ollie Watkins on David de Gea for the goal, I have never heard such tosh.
Did you know? Kortney Hause's winner for Aston Villa was his first goal in 22 away league games since scoring against Nottingham Forest in March 2019.
Dias: The block on Mateo Kovacic said it all. The way Dias flew across the penalty area at a crucial point in the game to block what looked like a certain goal was immense.
The Portugal defender was superb and looked like he was back to his best against Chelsea. The Blues, on the other hand, may have made a rather important mistake by selling Tammy Abraham to Roma and retaining the services of Timo Werner.
In the past I thought Werner might be the better option given the way Thomas Tuchel likes his teams to play but it would appear the German international suffers from acute stage fright and I don't think anyone can help him.
Did you know? Manchester City have conceded 22 goals in the 38 Premier League games Ruben Dias has featured in, having conceded 39 goals in 38 matches before his arrival.
Midfielders: Bukayo Saka (Arsenal), Jordan Henderson (Liverpool), Abdoulaye Doucoure (Everton), Emile Smith Rowe (Arsenal)
Saka: The ovation given to Saka after 87 minutes for his exploits in the north London derby said all you needed to know about his performance.
I said after his penalty miss in the final of the European Championships that it would be the making of him and I have seen nothing this season to change my mind.
Neither can it be overstated how important this result is for Mikel Arteta. Had he lost this game there is no telling what might have been the outcome. As it stands, it is now Nuno Espirito Santo's time to feel the heat.
Did you know? Arsenal's Bukayo Saka (aged 20 years and 21 days) is the youngest player in Premier League history to both score and assist in a north London derby - a record previously held by Cesc Fabregas.
Henderson: Liverpool's draw at Brentford was an extraordinary game to watch and yet I was struggling to find a player to select for my team. The match was littered with mistakes and moments of occasional brilliance.
I refuse to select defenders who concede three goals at home or away and strikers who miss more chances than they score - although I have to make an exception for Salah - which leaves me with Jordan Henderson.
Liverpool keep trying to write this lad off but when the Merseysiders hit the buffers, and they did against Brentford, Henderson is the one player they can depend on to see them through the crisis. An exceptional professional.
Did you know? Jordan Henderson made three key passes against Brentford - more than any other player in the match.
Doucoure: I saw this lad play for Watford and he was outstanding for them so I wasn't the least bit surprised when he turned up at Goodison Park.
Doucoure can run for fun and has the ability to score the occasional goal. When he does, they tend to be stunners. He was outstanding against a Norwich side who I have said on repeated occasions are doomed, but they did have a go at Everton.
What was interesting about this performance by the Toffees was, considering a number of big names were out of the side through injury, they put together a very creditable performance.
Did you know? Abdoulaye Doucoure scored his second Premier League goal in six games this season, as many as in 29 games in the 2020-21 campaign for the Toffees.
Smith Rowe: The writing was on the wall at Emirates Stadium when I saw Ben White outjump Harry Kane for a 50/50 header in the early exchanges. Anyone can lose a header but it's Kane's body language that worried me.
I said last week against Chelsea that he looked like he didn't fancy it, while against Arsenal he looked like he was going through the motions. I expect the captain of Tottenham Hotspur and England to be made of tougher stuff.
Meanwhile Arsenal have a 21-year-old in Smith Rowe who was prepared to walk over broken glass to win this derby. He said in his post-match interview that it was the best day of his life. Well I hope there are better days to come for this talented youngster. Just not at Tottenham's expense.
Did you know? Arsenal team-mates Emile Smith Rowe and Bukayo Saka have assisted one another five times in the Premier League. Of duos both aged 21 or younger, only Cristiano Ronaldo and Wayne Rooney (eight) have assisted one another more.
Forwards: Mohamed Salah (Liverpool), Raul Jimenez (Wolves), Michail Antonio (West Ham)
Salah: I'm almost irritated by my own selection. By Salah's standards, this was a poor performance from the Egyptian superstar.
He probably scored the easiest chance of the match. However it's very difficult to ignore a player who has scored 100 Premier League goals faster than any other Liverpool player in their history. It's a magnificent achievement even if the performance against Brentford wasn't one of his best.
Ten of the 11 Brentford players have played in every game this season and that is why they will eventually struggle to survive this season, although I think they just might make it.
Did you know? Only Alan Shearer at Blackburn (124), Harry Kane at Tottenham (138) and Sergio Aguero at Manchester City (147) have reached 100 Premier League goals for a single club in fewer appearances than Mohamed Salah at Liverpool (151).
Jimenez: I loved this goal. He won the challenge, beat the oncoming defender, collected himself and slotted the ball past the Southampton keeper as though he wasn't there.
Boy, have Wolves missed Raul Jimenez. I thought that last week when they played Brentford and the Mexico international missed a chance with his head and threw off his headband in anger and left it on the pitch. I was in no doubt at that moment that Jimenez was back mentally as well as physically.
The head injury he sustained against Arsenal last season took its toll but Jimenez seems back to his best and Wolves are in desperate need of him.
Did you know? Raul Jimenez scored his first Premier League goal in 336 days, since netting against Newcastle in October 2020.
Antonio: The ball from Antonio for Pablo Fornals earlier in West Ham's game against Leeds was just brilliant but his finish was indicative of a striker on top of his game.
He might have been player of the month for August but he was certainly man of the match against Leeds. The Jamaica international plays a very physical game but in front of goal there is also a touch of class as well.
When I first saw Antonio play he was like a bull in a china shop. Now he looks like a match-winner. I suppose that's what happens when you work at your game.
Did you know? Michail Antonio is the third player to score a 90th-minute winner against Leeds at Elland Road in the Premier League and the first since Scott Parker for Charlton in December 2002.
Pick your team of the week
Pick your XI from our list and share with your friends.
Select formationConfirm teamThe Crooks of the Matter
I have always had enormous respect for Arsene Wenger and thought he was treated appallingly by Arsenal fans prior to his departure. I've even gone on record to say that had Wenger been manager of Spurs they would have erected a stature of him by now.
However since his appointment as Fifa's head of global development he has catapulted himself into the international spotlight again in the most controversial circumstances.
The former Arsenal boss insists there is an appetite among less traditional football territories to hold the World Cup every two years. What Wenger is less keen to promote is that the most fans, across all age groups, prefer to maintain the status quo and host the tournament every four years. Meanwhile, the European and World League Forums have kicked this idea firmly into the stands.
So why would Wenger put his reputation on the line to support a proposal that neither the clubs nor fans seem to want?
One minute Fifa is prepared to expel some of the biggest clubs in the world for adopting a Super League that threatened the entire European domestic program; the next they are considering smashing it to smithereens themselves by proposing a World Cup every two years.
This is also the same organisation that was prepared to stop players who refused to travel to Covid-restricted areas to play for their national associations from earning their living and playing for their clubs.
This is less about the health and safety of players, or modernising the game, than it is a sophisticated power grab that will provide Fifa with greater control over the game's income streams.
- Our coverage of your Premier League club is bigger and better than ever before - follow your team and sign up for notifications in the BBC Sport app to make sure you never miss a moment