Philippe Coutinho scored the winning goal after City had fought back from 2-0 down with a superb first-time finish from the edge of the box 12 minutes from time after a blunder from Vincent Kompany as the Reds secured their 10th win in succession.
The Merseyside club, who paid tribute to the 96 supporters who lost their lives in the Hillsborough disaster 25 years ago prior to kick-off, now have a seven-point cushion on Manuel Pellegrini's men, although the Etihad side still have two games in hand.
Liverpool roared out of the blocks and took the lead with just six minutes on the clock as Raheem Sterling was picked out by Luis Suarez's excellent pass and the youngster showed incredible composure to bamboozle both Kompany and Joe Hart before rolling home.
Hart produced a superb save to deny Steven Gerrard's free header from Coutinho's corner, but the lead was doubled from the captain's resulting kick as Martin Skrtel got away from Kompany at the near post to glance home.
City hit back in style in the second half with David Silva (57) converting James Milner's low cross, before Glen Johnson could only divert the Spain international's shot beyond Simon Mignolet at his near post, but Liverpool were not to be denied, although Jordan Henderson saw red deep into added time.
After an impeccably observed minute's silence, the volume inside Anfield was soon cranked up and a clearly fired-up Suarez was booked early for a late challenge on Martin Demichelis.
The Uruguayan's next intervention was out of the top drawer as his brilliant through-ball put Sterling through to open the scoring.
After Sterling's teasing ball had been guided wide of the far post by Daniel Sturridge, there were more good omens for the hosts when Yaya Toure was forced off with an injury apparently sustained ballooning a shot into the Anfield Road end.
If City were all over the place before he departed they were almost clueless afterwards, allowing Gerrard a free header from a Coutinho corner which Hart superbly tipped over.
It only delayed the inevitable as from the resulting Gerrard corner Skrtel easily lost Kompany, nipped in front of Gael Clichy and flicked a header over Hart and inside the far post.
The speed of Liverpool's attacks had City chasing shadows - unfamiliar territory for them - and Coutinho, Suarez and Sturridge combined to almost make it three.
Gerrard, excellent in nullifying the first-half threat of Silva, produced the perfect tackle to deny Edin Dzeko inside the area, before Mamadou Sakho managed to get away with a less precise challenge on the Bosnian.
After Sterling and Johnson both cleared from under their own crossbar and Mignolet saved Fernandinho's volley, City hit back in the second half.
James Milner's introduction for Jesus Navas five minutes after half-time produced a positive response with the England international combining to allow Silva to expertly round off an incisive passing move.
Silva, finding greater freedom, created the equaliser when he drifted left and drilled in a low cross which Johnson diverted past Mignolet.
City were now in the ascendancy and Silva should have put them in front when substitute Sergio Aguero skipped past Skrtel and crossed to him but the Spaniard guided his shot wide.
It was to prove costly as a misjudgement by Kompany presented Coutinho with a chance which he drilled past Hart.
Liverpool were reduced to 10 men as Henderson lunged in on Nasri and was shown a straight red card by referee Mark Clattenburg.
They held on and the team huddle at the end, with an emotional Gerrard offering his words of wisdom accompanied by chants of 'We're gonna win the league', certainly put a smile on the face of watching owner John W Henry.