At the bottom, however, Sheffield United are cut adrift and yet to win this season, with the ignominy of a record-low points total a real possibility.
Here, the PA news agency looks at five things we learned from the top-flight action this weekend.
The most open title race for years?
Liverpool left their rivals in their wake last season, leading from the second weekend to be comfortably crowned champions at the finish. In fact after 16 matches last term, Jurgen Klopp’s side were already seven points clear of their closest challenger Leicester.
But the indications are that things will be very different in 2020-21. The Reds are top again but only on goal difference this time from great rivals Manchester United, with the two teams set to clash this month.
Leicester are just a point further back in third place, while Tottenham and Manchester City are four points behind Liverpool, with Pep Guardiola’s side lurking menacingly with a game in hand.
Chelsea slump continues
Chelsea were another team right in the mix until a few weeks ago. However, Sunday’s 3-1 home defeat to Manchester City was a fourth loss in six Premier League matches and has seen them slip seven points off the pace, having played a game more than all above them apart from Leicester.
Four points from the last six games is Chelsea’s worst run during Frank Lampard’s season-and-a-half in charge as manager and he must turn it around quickly if the Blues are to remain in touch and be considered title challengers.
Lampard’s team face big games in the coming weeks against Leicester and Tottenham.
Kane and Son combine again
Kane, who opened the scoring from the penalty spot, teed up the South Korean’s 100th goal for the club as the pair combined for a 13th time this term, matching the tally set by Alan Shearer and Chris Sutton at Blackburn in 1994-95.
They have been the story of the season for Spurs and are just four short of equalling the total record of 36 set by Didier Drogba and Frank Lampard while at Chelsea.
Their unison on Saturday was timely as their contribution helped Spurs end a four-game winless run in the Premier League, keeping Jose Mourinho’s men firmly in the title chase.
Three-sy does it for resurgent Gunners
Without a league win in seven attempts and having collected just two of the 21 points on offer in the process, Arsenal were being talked about as possible relegation fighters just before Christmas
However, a morale-boosting 3-1 win against London rivals Chelsea was followed by a solid success at Brighton, and Mikel Arteta’s team made it three straight Premier League victories for the first time since July with a rampant 4-0 win at West Brom.
Goals from Kieran Tierney, Bukayo Saka and Alexandre Lacazette’s double suggested the Gunners have what it will take to climb the table.
More misery for the Blades
Chris Wilder’s side were a revelation last season, finishing ninth on their return to the top flight, but they have struggled badly this time round. The Blades have lost 15 of their 17 matches and have made the worst start of any team to a Premier League season.
Their last win in the competition was 21 games ago, a 3-0 success over Chelsea at Bramall Lane on July 11, and the Blades face the distinct possibility of an unwanted record – a lower points total than Derby’s 11 during the 2007-08 campaign.