Roberto Mancini's 10 men survived a serious examination of their title credentials to extend their unbeaten league record to 13 matches.
Had it not been for goalkeeper Joe Hart the visitors may have tasted a league defeat for the first time since May 7.
They barely had time to celebrate Vincent Kompany's 31st-minute opener before Charlie Adam's shot was deflected in by Joleon Lescott.
In the second half, substitute Mario Balotelli lasted 18 minutes before being sent off for a second bookable offence and had England international Hart not been on top form, City would have succumbed to sustained Liverpool pressure in the final 20 minutes.
Having coasted serenely through the domestic campaign, scoring goals at will, this was the first time this season Mancini's side had failed to score more than once in a league match.
Credit must go to Liverpool who, after a slow start, enhanced their own reputation as genuine top-four contenders with a second-half performance which produced everything but a winning goal.
City may have previously won only once at Anfield in the last 30 years - and that in May 2003 - but they played the first half like they were the home team.
They passed the ball around with consummate ease, as they have done all season, with both Samir Nasri and David Silva threading threatening balls down the side of the two centre-backs.
Liverpool tried to employ the same high, pressing tactics which were so effective in last week's victory at Chelsea and it worked to some degree.
For all City's neat triangles and movement off the ball they did not really threaten and the closest they came was when they were gifted an opportunity by Jose Enrique's backpass.
The Spaniard was obviously unsighted when he rolled a ball too close to Sergio Aguero but Jose Reina raced 15 yards out of his penalty area to first block and then, after the ball rebounded off the Argentinian back onto his arm, clear.
Aguero was doing his best to unlock what is becoming an increasingly frugal Liverpool defence and he twisted past Martin Skrtel and Daniel Agger with ease on the left of the area but bamboozled himself and lost balance.
Ironically, considering the silky attacking skills at their disposal, the visitors took a 31st-minute lead from an old-fashioned corner routine.
Silva swung in a left-footed cross and centre-back Kompany glanced a header, which squirted off his shoulder, into the far corner after marker Dirk Kuyt and Glen Johnson got in each other's way.
That is usually the key for Mancini's side to go into attacking overdrive but within two minutes they found themselves pegged back as indecision and a bad decision cost them.
Kompany's weak clearance dropped to Kuyt who squared for Adam to unleash a left-footed drive which was heading wide until Lescott tried to clear and succeeded only in diverting past Hart.
If he was helpless to stop that shot the England goalkeeper showed his quality as he stuck out a leg to brilliantly divert Adam's right-footed shot over.
Suddenly the momentum was with the Reds and Johnson, last week's match-winner, flashed a left-footed shot past Hart's right-hand post.
Reina saved low from Aguero in first-half added time but the open football continued after the break as Stewart Downing's cross ballooned up off Kompany and Kuyt's diving header missed the target.
The languid, measured play of the first half had been replaced by a more frenetic approach after the break, evidenced by Hart's hurried punch to Downing's cross.
Hart did better with his England team-mate's shot into the turf from Adam's corner, tipping over just as the ball was about to dip under the crossbar.
The increasingly manic atmosphere hardly needed enhancing but the arrival of Balotelli for Nasri did exactly that.
Right on cue the Italian produced a comedic stumble, a fraction of a second after Skrtel had slipped trying to reach the ball, just when he was about to burst into the penalty area.
Liverpool had steadily grown more comfortable over the course of the game and they had the momentum entering the final 20 minutes.
Enrique and Downing shot wide before Balotelli's propensity for getting himself in trouble surfaced late on.
Having been booked for pulling back Johnson, he was shown a second yellow card for catching Skrtel across the face.
Hart kept his side in it with another good save at his near post from Luis Suarez before Silva over-complicated things in Liverpool's area having beaten Reina and Skrtel cleared off the line.
But Hart was the one being worked the hardest and another brilliant one-handed save from Andy Carroll's header in added time preserved City's unbeaten start.