Garth Crooks' team of the week: Stones, De Bruyne, Mane, Costa
Manchester City are the only Premier League side with their 100% start to the season intact after they beat derby rivals Manchester United to stay top of the table.
Liverpool beat champions Leicester City, while Arsenal, Bournemouth, Tottenham and Watford and Crystal Palace also won.
Chelsea were held at Swansea and you can see my team of the week above.
Do you agree with Garth's picks? Or would you go for a different team? Why not pick your very own Team of the Week from the shortlist selected by BBC Sport journalists and share it with your friends.
Goalkeeper - Steve Mandanda (Crystal Palace)
The Crystal Palace keeper has made a good start to his career at Selhurst Park and been unlucky not to have a better return for his efforts. However, against Middlesbrough the Frenchman was outstanding. Two saves from Negredo saved the day for Palace but it was his tip over the bar from Ben Gibson that was the most spectacular.
If the Eagles can produce the right service for Christian Benteke, and retain the £50m-valued Wilfried Zaha, then Palace seem almost certain to retain their Premier League status. Manager Alan Pardew's business in the transfer window has been outstanding. The acquisition of Mandanda, Benteke and Loic Remy has once again established Pardew's business acumen. If he were to get £50m for Zaha this season I suggest he gives up football and becomes the chairman of the Confederation of British Industry!
Right-back - Kyle Walker (Tottenham)
The move for Tottenham's third goal started in their penalty area and ended up in the back of the net. In fact Kyle Walker, who made this goal for Delli Alli, hadn't left the penalty area when Christian Eriksen made the break.
The speed at which Walker raced forward to support the Spurs attack was tremendous but it was also the ease and composure he showed when he gently stroked the ball for Alli to finish that really made me take note. I've seen Walker in this mood before and it bodes well for Tottenham's fortunes in the Champions League.
Defender - Laurent Koscielny (Arsenal)
When I saw Laurent Koscielny sitting in the stands recovering from his European Championship exploits when his team-mates were in desperate need of defenders against Liverpool, it made me question his commitment to Arsenal's cause. This is a player with enormous qualities and they were perfectly demonstrated against Southampton.
You don't often see a defender execute an overhead kick as well as Koscielny did to equalise against Southampton. If he is going to have a day off in future he should try to make sure it's not a matchday.
Defender - John Stones (Manchester City)
When Pep Guardiola brought John Stones to Manchester City for a king's ransom, few doubted his judgement and quite rightly so. However, if the performance of keeper Claudio Bravo against Manchester United is anything to go by then Stones may prove to be more valuable than originally thought.
Stones had to dig the debutant keeper out of so many situations against Manchester United I started to question whether Guardiola understood that in the Premier League the ball can arrive in the penalty area at any time and from anywhere. It doesn't matter how good a goalkeeper is with his feet - if he can't use his hands, what's the point?
Defender - Jose Holebas (Watford)
We all saw it. That wonderful reverse pass by Dimitri Payet that lead to West Ham's second goal. The only problem with moments like that is the media love them but they stick in the minds of pros who find such extravagances unnecessary and humiliating.
So I can only imagine the delight of the Watford players when they saw Payet in a heap after a perfectly legitimate tackle by Jose Holebas. In the same move Holebas went on to complete a proper humiliation by scoring Watford's definitive goal to complete West Ham's total demise. Now that's what I call revenge.
Midfielder - Adam Lallana (Liverpool)
At last Adam Lallana appears to be enjoying his game under the Anfield spotlight in the same way he did when he set the Premier League alight at St Mary's with Southampton. We've seen flashes of his brilliance but what I detect now is a player who has come to terms with the weight of expectancy that comes with being a Liverpool player.
The England international has finally realised that he is no longer playing at the Adelphi Theatre every week but Carnegie Hall. In the past, I sense he has struggled with this notion but it would seem not anymore. Lallana's all-round performance for club and country this week suggests that the player is finally coming to terms with the demands of playing for a big club and might even prove to be its leader in the end.
Midfielder - Kevin de Bruyne (Manchester City)
Manchester United boss Jose Mourinho didn't heed the warnings. The quality of Kevin de Bruyne's cross in the opening minutes against his side should have been enough to tell the Portuguese that De Bruyne had a score to settle. It was Mourinho who told De Bruyne he wasn't good enough at Chelsea and sent him packing with a career to rebuild.
De Bruyne has come back to the Premier League with a vengeance and tore the heart out of Mourinho's side in the derby. In fact, the Belgium international already looks like a contender for player of the season.
Midfielder - Son Heung-min (Tottenham)
I must say I thought Son's first goal was a bit opportunistic but his second was a wonder goal. Last season Spurs tore Stoke apart by four goals to nil, looked full of enterprise and guile and got us all talking about how they were title contenders. Well, I have no intention of falling for that again.
Striker - Sadio Mane (Liverpool)
Sadio Mane cut Leicester to ribbons. What excites me about this player is his change of pace. On two occasions Mane gave Kasper Schmeichel the impression that the keeper was the favourite to win the race to the ball and both times Mane switched on the turbochargers and left Schmeichel completely exposed.
There is a developing mood in the game that seems to encourage keepers to venture way beyond their penalty area in order for their defences to push high up the field. The only problem with that is it leaves the goal unprotected and the keeper looking rather foolish if it fails.
Striker - Diego Costa (Chelsea)
Recalled to the Spanish national team in midweek, the striker helped himself to two goals to justify his selection and another two against Swansea in the league in a pulsating game at the Liberty Stadium. The Chelsea hit man looks deadly in front of goal at the moment but still can't help causing mischief.
Pundits with a younger perspective tell me how much they enjoy the aggressive element to his game and, without it, he would be far less effective. What nonsense. The lad can play. Once you have that, do you need anything else?
Striker - Roberto Firmino (Liverpool)
With one Brazilian resting on the sidelines it was left to another to produce the goods. Philippe Coutinho will be the player who Liverpool depend on to see them past more difficult opposition but, in his absence, compatriot Roberto Firmino is very capable of holding the fort.
Firmino seemed to take great delight in putting Leicester to the sword. Meanwhile, the Foxes strike me as a team who have dispensed with the basic 'defend for our lives and then hit them on the break' attitude for a more sophisticated approach. The quicker Leicester get back to what they know, the better.