After just one point and no goals from two matches, they were given an easy ride at the Etihad Stadium on their way to opening up a cushion over their neighbours, who will try to reduce the gap again at Newcastle on Wednesday.
Despite their recent wobble Roberto Mancini's side are still a formidable force, especially at home, and they extended their 100% home league record this season to 10 matches and made it 55 points out of a possible 57 at the Etihad Stadium in the last year and three days.
It was only the second time this season Liverpool had conceded more than one in a league match - and their worst result since losing 4-0 at Tottenham in September - but it could easily have been more.
Sergio Aguero and Yaya Toure did the damage in the first half after benefiting from defensive lapses and even after Gareth Barry was sent off, City added a third with James Milner's penalty.
Mancini's side were fortunate to escape from Anfield with a 1-1 draw in November but this encounter was not even close as they recorded only their second win in 14 matches against the Merseysiders.
Prior to kick-off Liverpool confirmed they would not be appealing Luis Suarez's eight-match suspension for racially abusing Manchester United defender Patrice Evra.
If this is what life is like without the Uruguay international then the Reds could be in for a difficult six weeks, although the quality of opposition will rarely be matched.
In a battle between the league's top scorers and the meanest defence, something had to give but few would have predicted it would be the usually reliable Jose Reina.
Having already denied Edin Dzeko at the foot of his right-hand post, the Spain international made a complete hash of judging Aguero's 25-yard dipping shot and the ball flew underneath his body.
That was in sharp contrast to counterpart Joe Hart's reactions in denying Stewart Downing moments earlier when his England team-mate threatened to score having been played in by Jordan Henderson.
The goal had a more positive effect on Liverpool, who enjoyed their best spell of possession, than it did City but Reina was almost exposed again when Dzeko's shot deflected off Glen Johnson but crept just wide of the post with the goalkeeper completely wrong-footed.
While Liverpool were creating half-chances, with Hart pushing away Charlie Adam's low free-kick, City were more threatening thanks to the prompting of David Silva and Martin Skrtel was lucky to escape conceding a penalty when the ball bounced up on to his raised arm as Aguero tried to go past him.
Reina went some way to redeeming himself with a sharp save from Vincent Kompany's glancing header but was left helpless by Toure's powerful header off the underside of the crossbar from Silva's corner in the 34th minute.
Kompany showed his value at the other end of the pitch just before the interval by blocking Dirk Kuyt's close-range shot from Andy Carroll's knockdown.
In the technical area Reds boss Kenny Dalglish, hood up on his coat, gave the impression of a man trying to remain anonymous. Unfortunately for him most of his team had been equally nondescript in the first half.
Ten minutes into the second half Adam was replaced by Gerrard, who had been the catalyst for victory over Newcastle on Friday, and former City striker Craig Bellamy came on for Kuyt.
The substitutions produced the required lift but with City content to hold their lead and hit them on the break it remained a long way back for the Reds.
Liverpool appeared to have gained the momentum when Barry, having been booked late in the first half, was sent off for a second caution after blocking Daniel Agger.
But seconds later the result was wrapped up when they conceded possession inside City's half and Skrtel fouled Toure on the breakaway to allow Milner to make it 3-0 from the spot.
The hosts made their numerical disadvantage imperceptible and almost added a fourth when substitute Adam Johnson's shot beat Reina but rebounded off the post.
Gerrard responded with a long-range drive and substitute Maxi Rodriguez from much closer in but, like Liverpool's performance, they failed to hit the mark.
Even with the match won, City's concentration did not waver and Hart produced a point-blank block to deny Rodriguez.
The result highlighted the difference between title contenders and top-four hopefuls but worryingly for Liverpool they still have to face City twice more this month in the Carling Cup semi-final.