Leicester City continue to come closest to matching those top two this season, with the Foxes picking up the biggest win of the gameweek with a 5-0 drubbing of 10-man Newcastle United at the King Power Stadium.
Tottenham Hotspur were also reduced to 10 men but dug deep to grind out a 2-1 win over Southampton, while Manchester United and Arsenal fell further off the pace when they played out a low-quality 1-1 draw at Old Trafford on Monday night.
Chelsea picked up their first home league win under Frank Lampard by beating Brighton & Hove Albion 2-0, the same scoreline by which Crystal Palace and Wolverhampton Wanderers beat Norwich City and winless Watford respectively.
Here, Sports Mole selects its Premier League team of the week for gameweek seven.
There were clean sheets in half of the Premier League matches this weekend, but the standout goalkeeping performance came from Ederson, who went a long way to ensuring Man City did not fall further behind Liverpool. The Brazilian made six saves overall, including a couple of crucial ones to deny Yerry Mina on both occasions.
Wolves shot-stopper Rui Patricio deserves an honourable mention for his performance, as does his teammate Matt Doherty, but the right-back spot in this XI goes to Ricardo Pereira after he made it two goals in eight days with the opener against Newcastle - a driving run forward which was finished with aplomb.
Unsurprisingly, Leicester's five-star show makes them the best-represented club in this week's team, with Ben Chilwell also included on the opposite flank. The left-back was a constant presence going forward and also helped to mark Miguel Almiron out of the game.
It is not often two centre-backs from opposing teams in the same game both make our XI, but the defences were very much on top for Liverpool's trip to Bramall Lane. Sheffield United's back three performed admirably and were only undone by a goalkeeping howler, with John Egan the pick of the bunch having recovered possession 12 times, made four clearances and six interceptions, while only Fabinho made more tackles.
A more familiar name in the team of the week is Virgil van Dijk, who won more aerial duels than anyone else on the pitch in addition to making seven clearances and seven interceptions. On a day where the Liverpool attackers struggled to shine, it was Van Dijk who stood out for the league leaders.
Perhaps the best performance of the weekend as a whole came from Leicester's Wilfred Ndidi, who produced an outstanding all-round display against Newcastle. The Nigerian's 90th-minute goal capped off a showing in which he won nine tackles, made five interceptions and won the ball back 12 times.
There was plenty of competition for the holding midfield role this week, with Declan Rice and Luka Milivojevic also deserving mentions, and another contender is pushed into a slightly more attacking role with Jorginho continuing his revival of sorts under Lampard. The Italy international scored from the penalty spot and helped Chelsea dictate play for a welcome home win and clean sheet.
John McGinn makes it a goalscoring trio in the middle of the park this week, with the all-action Villa man scoring once and seeing another goal disallowed. The Scot has arguably been Villa's best player since their return to the top flight and this weekend edges out the likes of Kevin De Bruyne and Tanguy Ndombele to a place in the team.
Willian is the second Chelsea player in this week's team having ended his eight-month Premier League goal drought against Brighton, with his all-round performance enough to beat Joshua King to a place on the left, despite the Bournemouth striker having registered a goal and an assist.
On the opposite flank, Riyad Mahrez continues to stake his claim for a regular starting spot in Man City's front three, scoring their second goal against Everton to restore their lead with a pinpoint free kick. The Algerian has now been directly involved in 17 goals in his last 17 starts for the champions.
Leading the line this weekend is Mahrez's former Leicester teammate Jamie Vardy, whose brace against Newcastle now means that he has scored more Premier League goals than any other player since Brendan Rodgers's first game at the helm - a sign that he is well and truly back to his best. body check tags ::