They were one of three teams to spend a period at the top of the Premier League as the first Southampton took the lead following their Friday night win over Newcastle.
Tottenham replaced them thanks to late winner Harry Kane over struggling West Brom.
Elsewhere, Manchester United are back on their way to victory after coming from behind to see Everton in Merseyside.
But Arsenal were unable to save their impressive win at Old Trafford last week as they were blown away by Aston Villa.
Elsewhere, Crystal Palace and West Ham both got three points against newly promoted sides and Brighton shared the points with Burnley.
Here are our 10 talking points from the Premier League weekend of action …
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1. Klopp’s Courageous Appeal
After days of debate over whether Roberto Firmino or Diogo Jota would start Sunday’s game, Klopp surprised many by playing them both in a very offensive 4-2-4 formation.
It was a risk that certainly paid off initially, with Liverpool appearing far more inventive, menacing and dangerous than City throughout the vast majority of the first half.
The change in formation left them open and vulnerable to city counters every now and then, but that only added to what was a fascinating sight.
There is no doubt that Sadio Mane, Mo Salah, Firmino and Jota’s quadruple attacker is the one who just might tear up City’s weaker sides, and Reds fans have had a tantalizing glimpse of what may be to come. in the future.
2. The city needs a Walker upgrade
City right-back Walker looked like a man surpassing his best on Sunday.
Although he started the season rather well, the 30-year-old was coached by Mane at the Etihad and was awkward giving a penalty early on.
Roy Keane called Walker a “dumb” and “car crash” on Sky Sports at half-time, and while it sounds a bit harsh, it’s not the first time that the decision-making of the England international is called into question. .
Walker is not getting any younger and will surely continue to fight pacy attackers such as Mane even more as time goes on.
Guardiola has continued to stay loyal to Walker despite his mistakes in the past, but it may be time to look for another full-back option.
It will be interesting to see if City release their checkbook in January.
3. Where does that leave Solskjaer?
With Manchester United behind in the first half, the pressure on Ole Gunnar Solskjaer seemed to be reaching a critical point.
With the losses to Arsenal and Istanbul Basaksehir in memory, the trip to Goodison Park was billed as a must-see match for the Red Devils.
And after falling behind, they showed the character they’ve been missing in recent weeks to dig deep and lead through the gap.
As well as reversing the score, United have sucked Everton’s life out and shown barely noticeable control and dominance this season.
With Harry Maguire unwavering in defense, United weathered a flurry of late attacks from Everton and retained a vital victory that propelled them to 13th in the league.
The win sees United enter the international break on a positive note and with home games against West Brom and Istanbul Basaksehir after the break the Red Devils have the chance to secure a winning streak.
It could be a defining race for United’s season and Solskjaer’s future.
4. Pickford escapes punishment
Another game, another incredible decision from Jordan Pickford on set piece.
Dropped out for Robin Olsen in the previous match, Pickford was called up by Carlo Ancelotti for the Red Devils’ visit.
With his England No.1 status reaffirmed by Gareth Southgate midweek, it was an opportunity for Pickford to put his fragile form behind him.
To be sure, he could not have done much for either purpose; Bruno Fernandes’ header tucked into the top corner and he was lucky enough to see his cross go out of the post.
But Pickford produced another breathtaking second-half moment, releasing a free kick on the signing and proceeding to slam Harry Maguire as he tried to pounce on the stray ball.
The goalkeeper avoided punishment for the challenge and rallied well, making a good save to deny Marcus Rashford and claiming a dangerous cross.
But the mistake will lead to closer scrutiny of his status at club and country.
5. Wonderful Villa Form Guide
Southampton and Leeds had both put Villa to the sword at Villa Park in recent weeks so they had to fear the worst en route to the Emirates.
Arsenal looked like a million bucks as they dominated the Red Devils last Sunday and then they beat four goals in Europe on Thursday.
A formality? Think again.
Villa were fantastic from the first minute and looked like the whole side who won four on the rebound earlier this season.
Ross Barkley and Jack Grealish in particular caused all kinds of trouble for Arsenal and matched their quality with plenty of grafting.
And having a man like Watkins to finish their good job certainly makes life easier.
6. The struggles of Lacazette
It might seem strange to suggest that Arsenal’s top scorer is a man under pressure, but Lacazette hasn’t scored since September.
There are more and more calls for young Eddie Nketiah to replace the Frenchman in the top three.
And they will have regained momentum when Lacazette came from close in the first period with the Gunners looking for an equalizer.
Arteta demanded more goals from the 29-year-old and bought it for Nketiah on time.
Pierre-Emerick Aubameyang is a must-have despite his form and Willian has received a rave review from his manager this week, so if they go for a change of attack, there’s a good chance Lacazette will be the man sacrificed to the to come up.
7. Lookman is looking elsewhere
It already looks like Fulham will fight for his survival at the end of the season, which means every point counts, even at this early stage.
So when you get an added time penalty that lets you snatch a point, you take it.
West Ham and took a late lead at London Stadium, but Fulham received a penalty in the 97th minute after a VAR check.
Lookman stepped in and rather than hammering him with conviction, he did the unthinkable and tried to be smart.
He wandered around and tried to Panenka in the middle, but Lukasz Fabianski managed to reach out and save.
Fulham walked away empty-handed – how expensive could that be.
8. Jose and Tottenham go under the radar
Tottenham’s late show to the Hawthorns had this feeling – this feeling that Jose Mourinho could still have a little bit of magic.
The Portuguese boss has been questioned in recent years and has taken charge of a squad that are by no means considered true title challengers.
But maybe that’s why they’re so dangerous, because they can go under the radar.
Mourinho was allowed to bring some of his own faces this summer and started with Harry Kane, Gareth Bale and Son Heung-min for the first time.
It was Kane who scored three minutes from time to score his 150th Premier League goal.
Tottenham have been in the lead full time, only for a few hours, but that might not be the only time we’ve seen them lead.
9. Bamford’s VAR Nightmare
VAR was a big part of the weekend’s fixture list again, awarding several penalties for controversial handballs to King Power and then Etihad.
But without a doubt, he produced one of his most ridiculous decisions dismissing Patrick Bamford’s goal for Leeds against Crystal Palace.
The Whites were 1-0 at Selhurst Park when the forward indicated where he wanted the ball to be played.
He was clearly on the line when he got home, but he ignored his outstretched arm, indicating where he wanted the ball, counting against him.
His left shoulder was slightly in front of the last Palace defender once the lines were drawn.
It’s fair to say that the decision was not well received by the football world.
10. Leicester flies high despite a failed kick
Leicester reached the top of the Premier League on Sunday thanks to a Jamie Vardy penalty.
They could even afford the luxury of a miss kick from the striker as they began to show the kind of consistency that made them champions in 2016.
“Nine wins out of 11 show the team’s mentality. Our football has been exceptional against a very good team, ”Leicester boss Brendan Rodgers said after his side’s 1-0 win over Wolves, pointing to his side’s defensive resilience as praise.
If foxes can keep this solid shape, a new season of fairy tales just might take shape.
Who will finish in the top four this season? Give your opinion here.
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