One change was made from the previous win with Flanagan being replaced by Cissokho meaning 19-year-old Brad Smith was named among the substitutes but it was the hosts who had the better start as Navas looped a header that cannoned off the post and Kompany connected to a Nasri cross but failed to test Mignolet.
Liverpool had their first chance in the 14th minute when Suarez shot off target from Lucas' corner and the Uruguayan found Sterling and the winger rounded Hart to tap home only to be pulled back for offside even though it was clear he was onside so a massive error by the linesman could have proved costly.
However, Liverpool did take a valid lead in the 25th minute as Sterling picked out Coutinho and the Brazilian hit his first goal since his comeback from injury and City would have equalised instantly but Skrtel denied Toure with a fine challenge but Kompany rose highest to head past Mignolet and level the scoreline just after the half-hour.
Liverpool came close to regaining the lead with half-time on the horizon with a clever move from the trio of Suarez, Sterling and Coutinho splitting the City defence who had Hart to thank for denying Coutinho but City took the lead themselves as Negredo attempted to chip Mignolet and the Belgian got a hand to it but could not stop it from going in and meant City lead 2-1 at the break.
Henderson threatened to level early in the second half but hit narrowly over while Suarez evaded Zabaleta to force Hart to save impressively and the same duo were involved again as Sterling attempted to set up Henderson but the stray ball found Suarez who hit for goal but saw Henderson block the shot while offside.
Coutinho came off for Moses with 20 minutes to go as Liverpool pushed for an equaliser and could have had one had Johnson connected well to Henderson's cross and the midfielder went close himself but lacked the power to trouble Hart.
The visitors should have levelled in the 73rd minute when Suarez raced down the left and picked out Sterling but the winger could only hit over the bar after stretching to meet the cross and Liverpool pushed right until the final whistle but were unable to prevent City from continuing their unbeaten home record that saw Liverpool slip to fourth ahead of a trip to Chelsea.