Earlier, Manchester United thrashed defending Premier League champions Leicester City 4-1 to vindicate manager Jose Mourinho's decision to drop Wayne Rooney while Manchester City maintained their perfect start with a 3-1 win at Swansea City.
Arsenal scored twice in three minutes against a Chelsea defence missing injured captain John Terry with an ankle injury.
The Gunners were 1-0 up in the 11th minute when Alexis Sanchez robbed centre-back Gary Cahill and chipped the ball over goalkeeper Thibaut Courtois.
Minutes later it was 2-0 when Theo Walcott finished off a slick Arsenal passing move.
Arsenal, who hadn't beaten Chelsea in nine matches, were 3-0 up in the 40th minute when Mesut Ozil and Sanchez exchanged passes before the former volleyed home.
United scored four goals, three from set-pieces, as Chris Smalling, Juan Mata, Marcus Rashford and Paul Pogba -- with his first goal since his return from Juventus -- all found the back of the net between the 22nd and 42nd minutes at Old Trafford.
England skipper Rooney was limited to a few minutes off the bench but Mourinho told Sky Sports: "Wayne Rooney is a big player for me, United and this country."
Leicester managed a brilliant consolation goal from half-time substitute Demarai Gray but that could not stop the Foxes shipping four goals for the second time in as many away league games after doing so at Liverpool a fortnight ago.
"It's not possible to concede three goals off corners, that means you are not concentrating," said Foxes manager Claudio Ranieri.
Sergio Aguero marked his return from a three-game ban for a wayward elbow as Manchester City won 3-1 away to Swansea -- the second time in a week they had triumphed at the Liberty Stadium after their EFL Cup victory over the south Wales side.
Aguero fired City into a ninth-minute lead but Swansea were level minutes later when Fernando Llorente lashed in a half-volley.
City, however, regained the lead with an Aguero penalty in the 65th minute after Mike van der Hoorn fouled Kevin De Bruyne in the box.
Raheem Sterling, using Aguero as a decoy, made it 3-1 in the 77th minute.
"Sergio is quality," said Guardiola. "His first step, second step in the box is so good and that is why he is one of the best strikers in the world but I want to help him improve his game."
Liverpool overpowered Hull City 5-1 after the Tigers spent much of the match a man down at Anfield, with the Reds 3-0 up inside 36 minutes.
Adam Lallana put Liverpool ahead in the 17th minute and Hull then found themselves down a man when Ahmed Elmohamady was sent off after blocking Philippe Coutinho's goal-bound shot with his arm.
James Milner scored from the resulting penalty and Sadio Mane then made it 3-0.
David Meyler pulled a goal back before Coutinho scored with a brilliant 25-yard strike.
Milner scored his second penalty of the match after Daniel Sturridge was tripped by Andrew Robertson.
South Korea's Son Heung-Min scored twice inside the opening 23 minutes as Tottenham Hotspur, without injured England star Harry Kane, won 2-1 away to Middlesbrough, who pulled a goal back through Ben Gibson.
Spurs are second, four points behind leaders City and a point ahead of Arsenal, Liverpool and Everton.
Bournemouth ended Everton's unbeaten start to the season with a 1-0 home win secured by Junior Stanislas's superb shot into the top corner.
At the Stadium of Light, Crystal Palace came from 2-0 down to beat Sunderland 3-2.
Jermain Defoe seized on a mistake by Joe Ledley as he fired Sunderland into a 39th-minute lead and he then scored again on the hour mark.
A minute later, Ledley atoned for his earlier error with a goal and James McArthur headed in an equaliser before Christian Benteke's stoppage-time strike completed the south London club's comeback and denied Sunderland a first league win of the season.
Tony Pulis was unable to mark his 1,000th game as a manager with a win as his West Bromwich Albion side drew 1-1 away to former club Stoke City.
Joe Allen put Stoke ahead in the 73rd minute before Salomon Rondon equalised deep into stoppage time.
West Ham United play Southampton on Sunday and Monday sees Burnley at home to Watford.