These are the moments when Liverpool, to borrow a line from the kaleidoscope of colours on the Kop's banners, are making their supporters dream. When it really mattered, when the heat of the battle was dangerously close to intolerable, they found something extra just as it seemed everything was threatening to unravel. They played like champions and in the next few weeks that is feasibly what they will be.

Manchester City will chase them hard judging by the strength of their second-half recovery, and Liverpool still have to play Chelsea, who will be aggrieved by any suggestion that the title is all but confirmed for Anfield. Yet all the momentum is with Brendan Rodgers's team after this epic, coruscating match in which they still had the competitive courage to record their 10th straight win despite the jolt of seeing a 2-0 half-time lead wiped out.

What a moment it was for this club, commemorating the 25th anniversary of Hillsborough, when Philippe Coutinho drew back his right foot 12 minutes from the end to fire his shot inside Joe Hart's post. Rodgers was on the pitch in all the euphoria, in a modern-day re-enactment of Brian Kidd's famous celebration at Manchester United for the first of Sir Alex Ferguson's titles. This time Kidd was in the opposite dugout and, for City, it was a moment of real sporting trauma bearing in mind everything that had preceded it in the second half.

They had looked the more probable winners after David Silva had initiated the comeback, turning in James Milner's cut-back for the first goal and then supplying the cross from which Glen Johnson unwittingly skewed the ball into his own net. Milner's arrival as a substitute had changed the complexion of the game and Silva was outstanding in those moments when for the first time there was a sudden, damp silence to break the din.

City will look back with anguish on the chances Silva and Edin Dzeko passed up when the score was 2-2. They will also harbour legitimate grievances about a penalty appeal in each half and the referee, Mark Clattenburg's, failure to show Luis Suárez a second yellow card. Jordan Henderson was sent off in stoppage time for a studs-up lunge on Samir Nasri but Suárez, already booked, should have gone for a blatant dive.

Yet Manuel Pellegrini's team suffered because of the way they played in the opening half an hour, when most of the damage was done, and the gamble they took on Vincent Kompany's fitness, when his jarred knee could probably be held up as exhibit A in trying to explain why they defended with this much generosity. Kompany was still being assessed in the pre-match warm-up and was simply unable to exert his usual influence. He was at fault to varying degrees for all of Liverpool's goals and the third of them, when his sliced clearance went straight to Coutinho, was a personal ordeal.

Pellegrini could cite other mitigating factors on a day when Sergio Agüero was restricted to a substitute's role and Yaya Touré lasted only 19 minutes before being forced off with a groin injury. All the same, Liverpool's quick, attacking football overwhelmed their opponents in the early exchanges and, in a match of this significance, it was startling to see the way City crumpled.

Their manager had talked beforehand about the team with the "cold mind" winning the game. Yet Liverpool played as though filled with adrenaline and, again, Rodgers had assembled his team in a way to outfox one of their key rivals. Raheem Sterling's energy and directness, playing at the front of the midfield diamond, frequently exposed the absence of a classic defence-minded player in front of City's back four. Sterling's first instinct was to drive towards goal, playing as though absolutely immune to nerves, and it made him a constant menace for two centre-halves with the mobility of Martín Demichelis and a half-fit Kompany.

The tone was set after six minutes when Suárez brought down the ball, eluded Gaël Clichy with a Dalglish-esque jutting out of his backside and read his team-mate's run. Sterling darted behind the City defence, then delayed, and in one movement to the right took himself away from Kompany, as well as the oncoming Hart, before turning the ball into an exposed goal.

The breakthrough came so early it invigorated Liverpool, bringing almost unremitting pressure on the City goal. After 26 minutes, Hart kept out Steven Gerrard's header after Liverpool's captain had been left in an absurd amount of space from Coutinho's corner. City had not taken their warning. Gerrard swung over the resultant corner and Martin Skrtel was away from Kompany before flashing his header into the net.

City did not clear their heads until late in the first half and they did at least show great togetherness from that point onwards. It was a second half of relentless drama and, for a while, there was the distinct possibility that City, inspired by Silva, could complete the recovery.

Instead, there was one mistake too many from Kompany. Coutinho's finish was wonderfully taken and, at the final whistle, Gerrard had his team-mates in a scrum, making it absolutely clear they had to do exactly the same at Norwich next weekend.

The din was incredible – "old Liverpool", to apply the phrase Rodgers used – and the words carried so much importance here. "We're going to win the league," they sang.