Jurgen Klopp's team are now the only unbeaten team in the English top flight after their 4-0 demolition of Bournemouth, courtesy of a Mohamed Salah hat-trick.
Tottenham made it 12 wins out of 16 to remain in third place, while Chelsea's 2-0 win at Stamford Bridge kept them fourth.
Arsenal, in fifth spot, won 1-0 at home against Huddersfield while Manchester United took their place in the top six courtesy of a 4-1 romp at home.
Here are five things we learned from the Premier League this weekend:
Salah back in the groove
Mohamed Salah started his season slowly -- leading to inevitable questions about whether last season had been a flash in the pan.
But his hat-trick against Bournemouth on Saturday takes his Premier League tally to 10 for the campaign -- and the manner of his third goal in particular suggested his confidence is sky-high.
The Egypt forward, who scored 44 goals in all competitions last season, dribbled past Bournemouth goalkeeper Asmir Begovic twice before finishing coolly to put the gloss on an impressive Liverpool performance.
"Whatever you do in a football game, you need someone to finish it off," said Klopp. "What Mo did around his two goals in the second half was just exceptional. I don’t know at the moment a lot of players who would have scored these two goals."
Striker-less Man City not invincible
As Pep Guardiola predicted, Manchester City are not invincible. Chelsea rode their luck in the first half before emerging 2-0 victors at Stamford Bridge.
City now find themselves behind Liverpool in the title race despite being in imperious form for most of the season so far.
However, for all their much-vaunted strength in depth, City appeared to miss injured top scorer Sergio Aguero against Chelsea.
Guardiola left his only other natural striker, Gabriel Jesus, on the bench and City failed to take their chances despite dominating the first half.
Aguero is expected to return soon, but City's dependence on a 30-year-old with a history of injury problems offers Liverpool and the chasing pack hope.
Sarri challenges players
Going into their match against Manchester City, Chelsea had lost two out of three Premier League games after a bright start to the season and the players had incurred the wrath of Maurizio Sarri.
Now the Italian manager has challenged his players to follow up their win against City with a top performance against Brighton.
"We have a team with some difficulties to be motivated," he said. "In this kind of match (against City) it's very easy to have great motivation, determination, the right level of aggression."
"We need to play with this level of determination, with the right aggression in the other matches," he added. "Otherwise it's useless."
Spurs cope without Kane
Mauricio Pochettino's decision to leave Harry Kane out of Tottenham's starting line-up at Leicester underlined just how important victory at Barcelona and progress to the Champions League last 16 is for the Spurs boss.
Spurs made light of the absence of the England captain as Son Heung-min and Dele Alli came to the fore in a highly impressive 2-0 win.
Despite challenges on and off the field, Spurs are still ahead of Chelsea and Arsenal and just six points off the Premier League summit.
Mourinho sends Pogba message
Paul Pogba was an unused substitute as Manchester United won their first Premier League match in five attempts, scoring four goals in the process.
Romelu Lukaku was back in the starting line-up and scored his second goal in three games while Marcus Rashford netted just his third goal of the season for United.
"He has to play with the same mentality as the team is playing," Mourinho said when asked what Pogba needed to do to get back in the side.
"Paul can be a fantastic player, he has the potential to be a fantastic player. Against Valencia he is going to start and have a fantastic football game to play and to show everybody how good he is."