City dropped eight points behind unbeaten Chelsea by drawing 2-2 at lowly Queens Park Rangers thanks to two equalizers from Sergio Aguero, who is the league's top scorer with 12 goals.
Surprisingly, it is Southampton that is pushing Chelsea after 11 games, with a 2-0 win over Leicester leaving the south-coast club in second place and four points off the lead.
Chelsea, though, looks unstoppable.
Diego Costa scored the 67th-minute winner at Anfield, capping a Chelsea comeback that started in the 14th when Gary Cahill cancelled out a deflected opener from Emre Can.
"In the second half, we showed something new, which is to be 1-1 at Anfield and not accept the result as a good result and play to win," Chelsea manager Jose Mourinho said. "I think we were very impressive."
Elsewhere, Manchester United won 1-0 against Crystal Palace on Juan Mata's goal to climb provisionally to sixth, West Ham drew 0-0 at home to Aston Villa and Burnley recorded its first win in the league this season — 1-0 against Hull.
At Anfield, Liverpool manager Brendan Rodgers made seven changes from the side that lost 1-0 to Real Madrid in the Champions League on Tuesday.
His midweek selection was criticized as he appeared to prioritize the clash against Chelsea, and the gamble looked like it could pay off as Liverpool took the lead when Can's long-range strike deflected in off Cahill.
Chelsea equalized with a goal that required confirmation from goal-line technology, with Cahill blasting a shot from close range that goalkeeper Simon Mignolet saved before falling back over the line with the ball in his hands.
Costa's winner came when he pounced on the rebound after Cesar Azpilicueta's shot was parried out by Mignolet.
City fell behind at Loftus Road in the 21st when Charlie Austin converted from Mauricio Isla's cross. Austin earlier had two goals disallowed, one for offside and one after scoring directly from a mishit free kick by goalkeeper Joe Hart.
Hart accidently kicked the ball twice before Austin found the net, and rules state a player cannot touch the ball twice successively from a free kick.
Aguero equalized after brilliantly controlling a long pass from Eliaquim Mangala, but an own goal from Martin Demichelis in the 76th restored QPR's lead.
Argentina striker Aguero scored again seven minutes later, rounding Robert Green before beating four players on the line attempting to block his shot.
"Aguero had all the QPR defence in trouble whenever he had the ball," Pellegrini said, while QPR manager Harry Redknapp was left ruing his side's inability to hold on for victory.
"I really felt at 2-1 we would go on and win the game," Redknapp said. "You can't relax when they have got so many quality players in the team."
United earned a much-needed three points over Crystal Palace at Old Trafford thanks to Mata, who struck a deflected shot beating goalkeeper Julian Speroni four minutes after coming on as a replacement for Adnan Januzaj in the 63rd.
But it was another underwhelming performance from Louis van Gaal's team, which started with a makeshift defence that had midfielder Daley Blind and 19-year-old Paddy McNair at centre back with four alternative options injured or suspended.
The victory — United's first in four attempts — saw it overtake fierce rival Liverpool in the standings.
Southampton continued its formidable start to the season courtesy of two goals in five minutes from Shane Long at St. Mary's.
The Ireland striker, a substitute for Sadio Mane who had replaced him in the starting lineup, entered the game without a Premier League goal for Southampton since his off-season transfer from West Brom.
But he broke the deadlock in the 75th, curling a neat left-footed strike beyond Kasper Schmeichel, before finishing clinically past the Leicester goalkeeper for his second.
"It was difficult against a team who had very good organization in defence," Southampton manager Ronald Koeman said, adding that it was a tough decision to replace Long with Mane in the starting lineup.
"Sometimes Shane is not happy. Sometimes Sadio is not happy. It is a good reason to not be happy. Shane made the difference in the second half."