Manchester United thrashed Premier League champions Leicester City as boss Jose Mourinho dropped captain Wayne Rooney from his starting line-up.
Chris Smalling’s header put United ahead before Juan Mata finished off a slick move with a crisp strike.
Marcus Rashford and Paul Pogba – with his first goal for the club – both scored from corners, with Demarai Gray’s spectacular long-range strike the only consolation for Leicester.
Rooney came on in the 83rd minute.
United’s first Premier League win in a month was sealed by half-time, but a third defeat for Leicester already matches their total for the whole of last season.
Liverpool claimed a third straight Premier League win courtesy of an emphatic victory over 10-man Hull.
The Reds controlled the game and led through Adam Lallana’s low shot.
Ahmed Elmohamady saw red for handball in the box, with James Milner scoring from the spot before Sadio Mane added a third for the home side.
David Meyler lashed in for Hull but Philippe Coutinho’s long-range strike and a second Milner penalty underlined the home side’s dominance.
Jurgen Klopp’s side are now third in the table and the division’s second-top scorers behind Manchester City, with 16 goals in six matches – 11 of those coming in their past three.
In the time since Klopp took over on 8 October 2015, Liverpool have scored 71 goals, more than any other team over this period.
Premier League leaders Manchester City maintained their perfect start under Pep Guardiola with victory at Swansea.
Sergio Aguero fired the visitors in front before Fernando Llorente scored his first Swans goal with an emphatic half-volley four minutes later.
Aguero netted his second goal with a penalty after Mike van der Hoorn elbowed Kevin de Bruyne, who later limped with an hamstring injury.
Raheem Sterling added a classy third after a quick counter-attack.
Guardiola’s men had looked a little below par with the score 1-1 at half-time, but an authoritative display after the break underlined their title credentials.
The Spaniard becomes only the second manager to win his first six Premier League matches after Carlo Ancelotti, who did so as he led Chelsea to the title in 2009-10.
Swansea’s defeat, meanwhile, leaves them hovering above the relegation zone by one point – albeit after an improved performance which may have eased the pressure on beleaguered head coach Francesco Guidolin.
Arsenal produced a devastating first-half display to dismantle Chelsea and secure a fourth successive Premier League win.
Alexis Sanchez took advantage of Gary Cahill’s error to race clear and lift a composed finish over Thibaut Courtois after 11 minutes, and Theo Walcott completed a brilliant move to steer in Hector Bellerin’s pass three minutes later.
Mesut Ozil then left N’Golo Kante trailing to expose Chelsea on the counter-attack and steer home Arsenal’s third five minutes before the break, after an exchange with Sanchez.
It was little more than damage limitation for Chelsea after that as they fell to their second league loss in a row as rampant Arsenal moved third in the table.