Goals from Dejan Lovren, Mo Salah, Xherdan Shaqiri and Fabinho gave the Reds a comfortable Boxing Day victory at Anfield while a stunning strike from Ricardo Pereira saw City beaten 2-1 at the King Power Stadium.
City had led through an early Bernardo Silva goal but the danger signs were there when Jamie Vardy set up Marc Albrighton to head the equalizer before halftime.
A spell of prolonged City pressure looked set to give the visitor the three points it needed to keep pace with Liverpool until from a half cleared corner Pereira blasted an unstoppable shot past Ederson.
Fabian Delph's 89th minute red card completed a miserable afternoon for Pep Guardiola's team, who now trail Liverpool by seven points in third spot having lost successive matches.
"We have enough points to be champions, but the other teams make more, they are better than us at the moment," he said.
"The game was there but it took a fantastic goal to punish us," added Guardiola whose team romped to the title last season and looked firm favorite until a recent poor run.
Leicester manager Claude Puel, reportedly under pressure, has seen his team beat Chelsea and now Manchester City in successive games to move into seventh spot.
Meanwhile, Tottenham Hotspur maintained its emerging title challenge with a 5-0 rout of Bournemouth at Wembley, making it 11 goals in two games for Mauricio Pochettino's men, to leapfrog City into second place in the standings.
Bournemouth made the better start and might have taken the lead until a deflected Christian Eriksen strike put Spurs in front.
Son Heung-Min made it two and Lucas Moura, in for the injured Dele Alli, scored the third before halftime.
Son's second, to follow on from a double in the 6-2 rout of Everton, and a Harry Kane goal completed the scoring in the second half.
Solskjaer's dream start
The other highlight of a full program of fixtures was a first home win for Ole Gunnar Solskjaer as caretaker Manchester United boss as Paul Pogba netted twice in the 3-1 win over struggling Huddersfield.
Following on from the 5-1 away rout of Cardiff City in his first game in charge, Solskjaer is clearly relishing his new role after the sacking of Jose Mourinho following United's 3-1 defeat to Liverpool earlier this month.
A sluggish start at Old Trafford was enlivened by Nemanja Matic's tap-in after Victor Lindelof's header header had been cleared off the line in the 28th minute.
French World Cup star Pogba, sidelined by Mourinho before his departure, put the game out of Huddersfield's reach with two fine goals in the second half to underline his quality.
Mathias Jorgensen got a consolation for the Terriers just before the end.
"Paul knows he can score more goals and create chances," said Solskjaer, who admitted he was still finding his feet.
"I've not got used to it yet. It's humbling knowing I'm leading this team out."
Liverpool marching on
Liverpool's unbeaten start to the season was never seriously under threat from visiting Newcastle, managed by former boss Rafa Benitez.
The opener came from an unlikely source as central defender Dejan Lovren struck with a sweet half-volley on 11 minutes
The second came from the penalty spot as Mo Saleh converted after being pulled back by Paul Dummett early in the second half.
The influential Xherdan Shaqiri and Fabinho added the other goals in a comfortable win, the 16th of the season with three draws at its halfway point.
Klopp though, celebrating his 100th Liverpool win, is in no mood for complacency: "The six-point lead means nothing," he said.
"We have to win our games, we have to be focused, we really need to be in the mood with having tunnel vision."
Elsewhere, Everton rebounded from its defeat against Spurs to thrash Burnley 5-1 while Crystal Palace and Cardiff shared a goalless draw and Fulham was held 1-1 at home by Wolves.
In the late kick offs, Eden Hazard scored a double for Chelsea in a 2-1 win at Watford to move into fourth place, with Arsenal, in fifth, held 1-1 at Brighton.