Liverpool have maintained the English Premier League's only perfect record on with a clinical 3-1 win over Arsenal.
Joel Matip headed Liverpool into a first-half lead at Anfield and Mohamed Salah struck twice after the break on Saturday to give the Reds the maximum nine points at the top of the table and hand Arsenal their first defeat.
"After three games it doesn't say too much," Matip told Sky Sports.
"We are happy we've won the first three matches and now we are looking forward to Burnley [next week].
Patrick van Aanholt's goal in injury-time gave Crystal Palace a first-ever EPL victory over Manchester United 2-1, while Frank Lampard's first win as Chelsea manager came by a 3-2 success at Norwich City.
Leicester City went third with a 2-1 win at promoted Sheffield United, Southampton won 2-0 at 10-man Brighton & Hove Albion, and West Ham United won 3-1 at Watford in the day's other matches.
Arsenal looked set to reach halftime goalless only to have Matip head home a corner in the 41st minute.
Salah then settled things by striking twice early after the break, the first from a penalty and the second from a long run after getting past David Luiz.
Lucas Torreira scored a late consolation for Arsenal, who have lost their last seven visits to Anfield.
Daniel James looked to have earned Manchester United a point with a last-minute goal to cancel out Jordan Ayew's opener.
But van Aanholt stunned the Old Trafford faithful by beating David de Gea at the near post to secure a famous result for Palace.
"There is a first time for everything," the Dutchman told the BBC.
"I think we played really well. I think we deserved the three points."
Chelsea won for the first time under Lampard thanks to Tammy Abraham's brace.
Abraham and Mason Mount twice put Chelsea in front only to have Todd Cantwell and Teemu Pukki, with his fifth goal of the season, equalize in the opening 30 minutes.
Abraham struck the eventual winner in the 69th minute before Norwich's Ben Godfrey headed against the bar late on.
"I am very happy with the result because we are Chelsea, we want to win games," Lampard said.
"We had a tough start and I have been happy with a lot of the performances but you can't shout that too loudly if you are not winning games.
"I saw a really good belief in the players in the way they played today."
Goals from Jamie Vardy and Harvey Barnes earned Leicester a first win at Sheffield United, while new signing Sebastian Haller struck twice in the second half to get West Ham's maiden victory at bottom club Watford.
Moussa Djenepo and Nathan Redmond scored as Southampton win their first over Socceroos goalkeeper Mathew Ryan's Brighton, who had Florin Andone see red in the first half before they lost 2-0.
Champions Manchester City visit Bournemouth, Tottenham host Newcastle and Burnley are at Wolverhampton Wanderers on Sunday.
Australian Associated Press