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Ilkay Gundogan scored twice in the 4-1 rout of the champions in which Liverpool keeper Alisson suffered a horrible afternoon - making two dreadful errors to gift City two goals.
Chelsea's new coach Thomas Tuchel claimed his third win in four games since taking over from Frank Lampard, his side edging out bottom club Sheffield United 2-1 at Bramall Lane thanks to a strike by Mason Mount and a penalty by Jorginho.
Antonio Rudiger's own goal was the first goal Chelsea have conceded under Tuchel but it mattered not in the end as they moved up to fifth place, one point behind Liverpool who occupy the last Champions League berth.
Tottenham Hotspur snapped a three-match losing sequence with Harry Kane returning from a short lay-off because of an ankle injury to score his 208th goal for the club in a 2-0 win over West Bromwich Albion.
Kane is now joint-second on Tottenham's all-time scoring list alongside Bobby Smith.
Sunday's other game saw Wolverhampton Wanderers and Leicester City draw 0-0 - a result that left Leicester in third spot with 43 points, seven behind Manchester City.
Manchester United are second, five points adrift, after their 3-3 draw with Everton on Saturday.
Pep Guardiola's Manchester City side are beginning to look unstoppable, racking up a 10th successive league win and 14th in all competitions, although they were given a helping hand by Liverpool's usually reliable keeper Alisson.
Gundogan had put City ahead four minutes after the break only for Mohamed Salah to equalise for the Liverpool from the penalty spot after he had been fouled in the box.
Then the wheels fell off for Liverpool.
Twice in the space of three minutes Alisson misplaced passes out and was punished first by Gundogan and then by Raheem Sterling. Phil Foden lashed home City's fourth.
"It is an important win, but it is February. Of course, the gap to fifth is big right now and (qualifying] for the Champions League next season is important - but 10 wins in a row in this period is something exceptional," Guardiola said.
Liverpool manager Juergen Klopp said Alisson's two errors had proved costly.
"I saw a really good game and big mistakes. In each game, when you make these kind of mistakes, it's very likely you concede goals," Klopp said.
Tuchel has not even been in charge of Chelsea for two weeks but already they appear transformed.
Sunday's trip to a freezing Sheffield was a real test of their resolve, especially as United have been much improved of late including a win over Manchester United.
But they emerged with three points, although their winning penalty was awarded in bizarre circumstances.
Timo Werner was brought down by home keeper Aaron Ramsdale and while it looked a penalty the referee Kevin Friend waved play on until, almost two minutes later, he was instructed by VAR to give a penalty which Jorginho duly dispatched.
Hectic as his start in English football has been, Tuchel is clearly enjoying himself.
"The type of football is physical and tougher and there is a lot of quality and during matches it never stops," he said when asked for his thoughts in the Premier League.
"You feel absolute spirit to give everything in every match. It's a pleasure to coach every game because this is what we love and what I love. So far things are going well."