Manchester City 1 Liverpool 4: Coutinho and Firmino keep Pellegrini's side off summit
Liverpool produced an incisive attacking display to make the most of some dreadful defending from Manchester City and pick up a 4-1 victory at the Etihad Stadium.
Jurgen Klopp's side were clinical on the counter-attack, racing into a three-goal lead that brought an end to a run of six Premier League matches away at City without a win.
Eliaquim Mangala – brought into the centre of defence along with Martin Demichelis as two of Manuel Pellegrini's four changes – opened the scoring with an own goal early on, setting the tone for a dismal defensive display.
Philippe Coutinho scored his fourth goal in five top-flight appearances against City to double Liverpool's advantage, with Roberto Firmino – in for Christian Benteke as one of Klopp's three changes – adding the third in sensational fashion.
Making his return after a seven-week absence, Sergio Aguero brilliantly pulled one back for City shortly before the interval, but they were unable to push on in the second half.
Their misery was compounded nine minutes from time when Martin Skrtel blasted past Joe Hart from the edge of the box, meaning City now sit third behind rivals Manchester United and shock leaders Leicester City.
Mangala got off to a poor start on his return to the starting line-up, putting the ball into the back of his own net off a cutback from Firmino, though Bacary Sagna was partly culpable having lost possession beforehand.
Liverpool grabbed their second when a mix-up between Mangala and Aleksandar Kolarov was capitalised upon by Firmino, racing through and picking out Coutinho with a sublime pass which he slid between Hart's legs.
In contrast, Liverpool's defence was proving extremely resilient and their counter-attacking play continued to trouble Pellegrini's side.
Another break led to their third shortly after the half-hour mark, when Emre Can's backheel set Coutinho in behind the defence and he squared for Firmino to round off an exquisite move with the simplest of finishes.
The former Hoffenheim forward came close to adding to his tally twice in quick succession soon after, first being denied by a good save from Hart before firing narrowly wide nine minutes before the break.
Aguero gave City a lifeline two minutes before the interval when he curled home an exceptional finish from 25 yards, becoming the highest-scoring South American in Premier League history with his 85th goal.
Pellegrini replaced Yaya Toure and Jesus Navas with Fernandinho and Fabian Delph for the second half in a bid to add more solidity to his team.
However, it compromised their creativity and they were carved open once again on the hour-mark, but Hart made a vital save to deny Firmino once more.
Klopp's side suffered a wobble moments later, Simon Mignolet forced into a diving save to keep Aguero at bay before Fernandinho skied an effort from six yards out off a set-piece delivery.
Skrtel fired home a powerful fourth from just inside the box and City's day was summed up when Raheem Sterling – facing his former employers – failed to make contact with the goal at his mercy as Liverpool moved up to ninth.