Roberto Firmino scored twice from Trent Alexander-Arnold crosses either side of James Milner's penalty before the brilliant Alexander-Arnold rounded off the scoring himself.
James Milner said he would be delighted if Manchester United did Liverpool a favour in the Manchester derby at Old Trafford.
Liverpool now hold a two-point lead over City, but the defending champions have a game in hand.
Despite late drama, victory was well deserved for Liverpool who dominated throughout and bounced back from blowing a 2-0 first-half lead.
James Milner, Adam Lallana and Nathaniel Clyne took it upon themselves to inspire Alastair Cook & Co. ahead of the third Ashes Test.
England midfielder James Milner, who joined on a free transfer last month from Manchester City, was on target in the 67th minute for the second time in four days for Liverpool in Australia.
James Milner, the 29-year-old, capped 53 times by his country, will join Liverpool on July 1 after his Manchester City contract expires. Liverpool have not disclosed the length of his contract.
As Manchester City look for a second title in three seasons, Milner feels that the visit of Liverpool, and the following home game against Crystal Palace, offer City a real opportunity to take charge in the title race.
City came from 2-0 down to beat the reigning European champions 3-2. Real Madrid beat Copenhagen 2-0, with Ronaldo scoring to set a new record of nine goals in one group-stage campaign.
England midfielder Milner says Pellegrini, who guided Malaga to the quarter-finals of the Champions League last season, wants City to be more solid at the back before worrying about their attacking play.
City midfielder Gareth Barry felt that the team's fitness had let them down against Supersport United in Pretoria on Sunday.
The result ended United's four and a half month unbeaten run in the league and will retrieve some local pride for the champions. It surely came too late, though, to have any effect on the destination of the title.
England manager Roy Hodgson had called Ferdinand up for the first time for the upcoming World Cup qualifiers against San Marino and Montenegro, only for the 34-year-old to pull out, citing fitness concerns.
Premier League champions Manchester City remained seven points adrift of leaders Manchester United after a 2-0 win away to Arsenal on Sunday, with both teams finishing a man down in an eventful match.
Sergio Aguero justified Roberto Mancini's decision to haul off Mario Balotelli as the Manchester City striker came on to score the crucial goal in his side's 3-0 win over Sunderland on Saturday.
England will attempt to reach the last four of a major tournament for the first time in 16 years on Sunday as they face Italy in a heavyweight Euro 2012 quarter-final collision.
Theo Walcott praised England's attacking spirit after inspiring the fightback which helped his team to victory over Sweden.
James Milner has promised Manchester City will fight for the English Premier League title until they have no mathematical chance of being crowned champions.