Tottenham leapfrog City into second after thrashing Bournemouth 5-0, while Manchester United's perfect start under caretaker manager Ole Gunnar Solskjaer continued with Paul Pogba scoring twice in a 3-1 win over Huddersfield.
United remain eight points off the top four as Eden Hazard scored twice in Chelsea's 2-1 win at Watford, but fifth-placed Arsenal could only manage a 1-1 draw at Brighton.
Liverpool manager Jurgen Klopp has tried in recent days to stress that it is still far too early for his side to be talking of ending a near three-decade wait to win the title in December.
However, another routine win and a 12th clean sheet in 19 Premier League games will do little to dampen expectations ahead of a huge week for Liverpool with Arsenal visiting Anfield on Saturday before a visit to City on January 3.
"The six-point lead means nothing," insisted Klopp. "We play Arsenal and City. It's good that we have six points more than other teams, or seven, but that is pretty much all.
"What we wanted to do all the time was create a basis for the rest of the season. Now the first part of the season is over. We want to create our own history."
After a slow start Liverpool went in front through an unlikely source when Dejan Lovren volleyed home after 12 minutes.
It was a far more familiar marksman who made the game safe when Mohamed Salah scored from the penalty spot before Xherdan Shaqiri and Fabinho's first Liverpool goal rounded off the scoring.
City need confidence back
City boss Pep Guardiola made three changes from the side that lost 3-2 to Crystal Palace on Saturday with Sergio Aguero and Kevin De Bruyne returning, but even they couldn't prevent a third defeat in four Premier League games.
"We have to accept it, we have to realise that we have to work harder and try to get immediately one good result and get our confidence back," said Guardiola.
Aguero set up Bernardo Silva to give the champions a perfect start, but Marc Albrighton levelled just five minutes later.
City dominated possession throughout, but after Andros Townsend's incredible volley for Palace on Saturday they were hit by another wonder strike when Ricardo Pereira fired home nine minutes from time.
A terrible afternoon for City was compounded late on by a red card for Fabian Delph.
Spurs run riot again
As City flounder, Spurs are firing back into the title race as Mauricio Pochettino's men have now scored 11 goals in four days.
"We are in a very good position, but Liverpool and Manchester City are the real contenders," claimed a cautious Pochettino.
Fresh from a 6-2 hammering of Everton, Christian Eriksen, Son Heung-min and Lucas Moura put Tottenham 3-0 up before half-time at Wembley.
Harry Kane then got his goal just after the hour mark before Son recorded his second double in as many games.
Pogba was again to the fore as Solskjaer's dream start continued unabated in his first outing in charge at Old Trafford.
Nemanja Matic tapped home from close range to give the hosts a half-time advantage.
After providing three assists on his return to the starting line-up in a 5-1 win at Cardiff at the weekend Pogba showed the goalscoring threat he also poses from midfield by striking twice in 14 second-half minutes.
"That's the Paul I know," said Solskjaer," said Solskjaer. "He has always been a happy boy, he's always had a big smile on his face."
"When you play football for Man United you should be happy. Of course it's a responsibility, but it's an honour and a privilege."
Pierre-Emerick Aubameyang moved back ahead of Salah and Kane in the race for the golden boot to hand Arsenal an early lead at Brighton, but Jurgen Locadia pounced on a poor defensive header by Stephan Lichtsteiner to level just before half-time.
Chelsea are two points ahead of the Gunners as Hazard scored his 100th and 101st goals for the club to beat a spirited Watford at Vicarage Road.
"100th and 101st goals with this amazing club is something I will never forget," said the Belgian.
"I want to score more goals for this club and be a legend like (Frank) Lampard, (John) Terry or (Didier) Drogba."
Everton bounced back from their Tottenham thrashing by inflicting similar punishment on Burnley with a 5-1 victory at Turf Moor.
At the bottom Cardiff moved three points clear of the relegation zone by holding out for a 0-0 draw at Crystal Palace.
But Fulham remain rooted in the bottom three as Wolves struck late to secure a share of the points in a 1-1 draw at Craven Cottage.