Firmino and Liverpool punish sluggish Man City

City were bidding to return to first place after being usurped by Leicester City earlier in the day, but they were left in third after a sloppy and unfocused display at the Etihad Stadium culminated in their third defeat of the campaign.

Raheem Sterling, playing against Liverpool for the first time since his acrimonious close-season exit, had been the focus of the pre-match build-up, but it was Firmino, a £29 million ($44.1 million, 41.4 million euros) capture from Hoffenheim, who stole the headlines.

The Brazil international created an own goal by Eliaquim Mangala, teed up Philippe Coutinho and scored himself, all inside the first 32 minutes, and although Sergio Aguero marked his return from a seven-game lay-off with a hamstring injury by replying, Martin Skrtel slammed home Liverpool's fourth late on.

Klopp's side, beaten 2-1 at home by Crystal Palace in their previous outing, have now won away at Chelsea and City, although they rose just one place in the standings to ninth.

Prior to kick-off several Tricolores were held aloft during the playing of the French national anthem, in tribute to the victims of last week's Paris attacks, and City's France internationals Bacary Sagna and Eliaquim Mangala were both shown singing along on the stadium's big screens.

The pair could have been forgiven for having their minds elsewhere and that appeared to be the case as a sequence of glaring errors in City's defence allowed the visitors to take control of the game.

Liverpool went ahead in the seventh minute after Coutinho dispossessed Sagna and found Firmino, whose low cross was inadvertently scuffed in at the near post by the back-pedalling Mangala.

City manager Manuel Pellegrini had changed both his centre-backs, Mangala and Martin Demichelis starting in place of Nicolas Otamendi and injured skipper Vincent Kompany, and it was from a mix-up between the two newcomers that Liverpool added a second goal in the 23rd minute.

As both players converged on a loose ball, Demichelis contrived to head it past Mangala and Firmino squared for Coutinho to steer a shot between the legs of Joe Hart.

- Calamitous back-pass -

Liverpool were playing with an aggressivity and purpose that has characterised their approach since Klopp's arrival and they swelled their lead yet further after a sweeping counter-attack.

Coutinho initially saw a shot parried by Hart, but an audacious back-heel by Emre Can gave the Brazilian a second bite at the cherry and he rolled square for Firmino to tap home.

Firmino twice went close to compounding City's misery, first seeing an effort blocked by Hart and then hooking inches wide from Coutinho's flick.

Each misplaced pass from a player in sky blue drew a flurry of invective from the home fans, but shortly before half-time Aguero gave them hope.

The Argentine picked up the ball midway inside the Liverpool half, resisted the attentions of Adam Lallana and arced a right-foot shot around Simon Mignolet from 25 yards.

Pellegrini took reparative action at half-time, sending on Fabian Delph and Fernandinho for Yaya Toure and Jesus Navas in a bid to go toe-to-toe with Liverpool's three-man midfield.

His side remained troublingly porous at the back, however, and Hart was required to save with his right leg on the hour after Can's pass, dummied by Lallana, gave Firmino yet another sight of goal.

Hart also had to save from Dejan Lovren, before a calamitous back-pass from old boy James Milner almost let City back into the game, only for Mignolet to deny Aguero from Sterling's lay-off.

After Hart had thwarted substitute Christian Benteke, Skrtel slammed home from a corner to rubber-stamp Liverpool's first league win at the Etihad since October 2008 and condemn City to a second 4-1 reverse of the campaign after September's drubbing at Tottenham Hotspur.