Manchester City bounced back from their midweek setback in Europe to maintain their perfect Premier League start with Erling Haaland's double propelling them to a 3-2 home win over Ipswich Town on Saturday.
Paris St Germain inflicted a first meaningful defeat on Enzo Maresca's side in the Champions League on Wednesday but City shrugged off a gallant Ipswich side to make it seven wins from seven to cement their place at the top of the table.
Chelsea beat Everton 2-0 in Saturday's early action thanks to Pedro Neto's brace although the London club's win was overshadowed by an injury to goalkeeper Emi Martinez.
Liverpool came from a goal down to beat Brentford 2-1 away although they were helped by the previously unbeaten hosts being reduced to 10 men shortly before halftime when Yehor Yarmolyuk was shown a straight red card for a head butt.
Victory lifted Liverpool above Brentford into fifth place with 12 points behind Chelsea in fourth on 13.
Fulham moved off the foot of the table with their first league win of the season - 1-0 at home to Hull City.
Dark clouds remain over the Etihad Stadium with Manchester City's fate still unknown after they appealed a ruling that the club breached 114 Premier League financial rules.
City have always denied any wrongdoing.
But on the pitch it is very much business as usual, especially for Norwegian goal machine Haaland.
Phil Foden gave City a short-lived lead cancelled out by Daizen Maeda, but Haaland restored the home side's advantage before halftime with a header from Mateo Kovacic's cross.
Haaland then gave his side some breathing space with his second in the 69th minute, powering past Ipswich's Abdoul Ouattara before a low finish into the corner.
He was denied a hat-trick by an offside decision and Ipswich got a lifeline when Zian Flemming tucked away a penalty in stoppage time but City bagged the points.
Feisty First Half
Chelsea have had a knack of scoring early this season but were kept at bay by hosts Everton in a feisty and physical first half that produced five yellow cards.
However, Xabi Alonso's visitors needed just 43 seconds after the restart to go 1-0 up when Jorrel Hato cut the ball back from the byline to find Neto who swept home.
Martinez's clash of heads with Jarrad Branthwaite caused a lengthy stoppage with paramedics coming onto the pitch. The Argentina keeper was eventually strapped to a stretcher and taken off, leading to 11 minutes of stoppage time.
Chelsea doubled their lead in the 90th minute when Neto pounced on a loose ball after Jordan Henderson's free kick was blocked by the wall, finding the bottom corner with a composed finish as Everton suffered their first defeat of the season.
"What we know is he (Martinez) left the stadium conscious and right now he is in the hospital doing precautionary tests," Alonso said. "It was concussion but more than that I saw only one clip. Hopefully it won't be too bad but we need to wait."
Martinez's knock gave 21-year-old keeper Mike Penders the chance to make his Premier League debut and he helped Chelsea keep a clean sheet in the league for the first time in 23 games.
"We need a clean sheet, to be honest. I think we did a very good game. Emi deserved this, Mike did as well," Alonso added.
Liverpool deservedly fell behind at Brentford with Keane Lewis-Potter putting the hosts in front.
Brentford were good value for their lead but Yarmolyuk's rush of blood to the head when he clashed with Jeremy Jacquet at a Liverpool corner changed the game.
After referee John Brooks was invited to check a VAR monitor he brandished the red card at Ukrainian Yarmolyuk who trudged off to applause from the home fans.
Liverpool huffed and puffed after the break but Victor Munoz finally levelled in the 62nd minute when he cut in to beat keeper Caoimhin Kelleher with a left-foot finish.
Alexander Isak won it for Andoni Iraola's side eight minutes later with a clinical strike from Bradley Barcola's assist.
Brentford ended with nine men after Vitaly Janelt got a second yellow card for a foul on substitute Rio Ngumoha.
Alex Iwobi's 33rd-minute strike for Fulham was enough to earn their new manager Alvaro Arbeloa a long-overdue league win and move Fulham up to 15th.
Newcastle United welcome Aston Villa later on Saturday.