2015 unbeaten Reds beat City 2-1
Both sides suffered desperately disappointing defeats in Europe this week and will be keen to return to form in a massive EPL clash
Liverpool move up to fifth spot with win.
Reds unbeaten in the league in 2015.
City without a win at Anfield since May 2003.
Pellegrini's side remain five points behind Chelsea.
Philippe Coutinho scored a stunning winner as Liverpool dented Manchester City's Premier League title defence with a narrow victory at Anfield.
Jordan Henderson's curling effort put the Reds ahead before Edin Dzeko finished off a slick move to equalise.
But Brazil midfielder Coutinho capped a fine display with the decisive goal when he struck from 25 yards.
The result leaves City five points behind Chelsea having played a game extra, while Liverpool move to fifth.
Liverpool's 3-2 victory in this fixture last April was seen as a pivotal moment for the Reds in last season's title charge, although ultimately it was City that went on to win the Premier League a month later.
With Premier League leaders Chelsea in League Cup final action against Tottenham, City manager Manuel Pellegrini had underlined the importance of this match and the need for his side to "keep fighting" in the title race.
City made a two-point gain on Chelsea last weekend but they were unable to make up further ground on Jose Mourinho's side.
For Liverpool, it kept their unbeaten record league in 2015 and having taken 26 points from possible 30 momentum appears to be building in their bid to finish in one of the Champions League places.
Liverpool 2-1 Manchester City
Liverpool only arrived back at 4.30am on Friday following their penalty shootout defeat by Besiktas in the Europa League last week, and despite the physical toils of their travels Rodgers felt his players would be "mentally ready" to face City.
They showed few signs of tiredness, although it was Coutinho, rested for last week's trip to Istanbul, who was at the heart of Liverpool's attacking play.
Coutinho's sharpness helped Liverpool take an 11th-minute lead when he stole the ball off Vincent Kompany, making his 200th league appearance for City, and Raheem Sterling slipped the ball out wide to Henderson.
The England midfielder, who wore the Liverpool captain's armband in the absence of the injured Steven Gerrard, cut inside onto his favoured right foot and curled a stunning shot past Joe Hart and into the top right corner of the net.
The goal brought greater urgency to City's play and they almost equalised when Sergio Aguero latched on to David Silva's through ball only for the Argentine forward's shot to rebound off the post.
City got themselves on level terms before the half-hour mark with a slick move that culminated in Aguero's clever pass into the area for Dzeko and he clinically dispatched a low shot past Simon Mignolet in the Liverpool goal.
Aguero headed over from a dangerous position shortly after half-time, while Liverpool's Adam Lallana had the ball in the net again when he glanced in a free-kick only for the officials to judge he did so from an offside position.
Coutinho always seemed Liverpool's most likely source of another goal and he put the Reds ahead with a strike akin to the quality of the one he scored in their 2-0 win against Southampton last Sunday.
The playmaker jinked in from the left flank jinked and curled a spectacular shot past Hart and into the top right corner of the net in front of the Kop.
By Timothy Abraham