Game on. At a frantic, slightly wild Etihad Stadium Manchester City defibrillated their own hopes of retaining the title with a 2-1 defeat of Liverpool that was by turns fearful, fretful and often funny.

That they did so owed much to their fighting spirit, a little more to good fortune and even more to Sergio Agüero, the blue-grey rinse at the front of this team who played for 45 minutes like the only City player not afraid of the moment, still cold and cool in the middle of all that fury – of which there was quite a lot.

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No doubt there will be some talk now of City learning to win ugly. Incorrectly so. City did not win ugly here. They won very ugly. They also won slapstick, won zany and won thanks to something close to a pastiche of backs-to-the wall defending, coming on towards the end like a team of senior nuclear particle physicists caught up in an increasingly convincing bare-knuckle street brawl.

Finally one could almost hear the voices from the fringes muttering, as City’s ball-players experimented with the idea of shanking wild-eyed clearances into the crowd, as they punted the poor old beleaguered ball forward, as the back four lined up to head clear of their own six-yard box like a £900m Tony Pulis tribute project, and as Bernardo Silva, a man born to glide and twirl and address the ball with his own feather-quilled left foot, careered about the place like a city-centre nightclub bouncer on New Year’s Eve. Finally they have worked out how to play some proper football.

And yet for all the energy this was also a victory born out of precision and out of a moment of stillness from City’s most understated leader.

Facebook Twitter Pinterest Sergio Agüero eludes Dejan Lovren to blast in Manchester City’s opening goal. Photograph: Jon Super/AP

The images of victory will be rooted elsewhere. Vincent Kompany was at times a cartoon of chest-heaving full-body defence, although he might also have been sent off for an excessively forceful lunge through Mohamed Salah. At the end, as City’s players left the pitch, a teenage fan came haring through the lines to plead for a selfie with the captain and one half expected Kompany to take him out with a headlock-slamming two-footed Bruce Lee neck-lunge.

Beyond this there was Agüero, who came out to fight at the start when the rest of his teammates were cowed, and who produced the one real moment of precision in a fearful first half. Sometimes it really is about the inch in front of your face. Or at least, that inch in front of Dejan Lovren inside the penalty area, with the ball falling out of the sky, the goal at a narrow angle, and 52,000 people drawing half a breath.

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Play Video 1:42 Manchester City 2-1 Liverpool: Jürgen Klopp and Pep Guardiola react – video

City had struggled in the opening 40 minutes. Jürgen Klopp had gone with his most muscular midfield, that Milner-Henderson fulcrum, the footballing equivalent of a four-course all-you-can eat carvery roast dinner with boiled and mashed potatoes, all washed down with a two litre jug of extra thick custard.

It was a concussive, bruising affair in those early exchanges. Fernandinho ran through the back of Sadio Mané. Virgil van Dijk clobbered Agüero. Fernandinho expanded his range by forearm-clubbing Andy Robertson in the neck. On his touchline Pep Guardiola whirled his arms and crouched like a downhill skier, performing elaborate windscreen-wiper gestures, punching buttons, as though trying to draw his players closer together in front of him.

There was something missing from City in those moments. One could feel it stalking the pitch, an absence, something just out of sight. City had come without their swagger, more timid in the early minutes than they have been at any time in the last year and a half.

And Liverpool really should have scored on 17 minutes. How they did not will perhaps be the subject one day of a 38-volume Warren Report style investigation that still leaves room for conspiracy theories and mass paranoia. Somehow John Stones cleared on the line just as the ball seemed to have already bulged the net, Mané having rolled it on to the post from Salah’s beautifully nudged pass. Inches, again.

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It was Agüero who led City through this, a beacon of certainty from the front, dropping so deep he was upended a couple of times in his own half, taking the ball and turning in half spaces. He touched the ball 20 times in the first half, scarcely wasted a pass and moved with a kind of affronted aristocratic grace through the hesitancy behind him.

When the moment came he was ready. City pressed down the left. Bernardo Silva crossed from the touchline. Agüero stole in front of Lovren, took a touch and pirouetted towards goal. He did not look up as the ball dropped out of the lights, had already noted, logged and plotted the small pocket of space just past Alisson’s right ear, into which he spanked the ball with such sweetness it bulged along the roof of the net, rippling it out in cinematic fashion.

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The goal did settle City, although Roberto Firmino’s second-half equaliser was deserved and beautifully worked by Liverpool. City still had enough left to take the lead again, Leroy Sané’s shot skimming across Alisson into the far corner. And for all the fight and fury and grappling towards the end it was that moment of calm from their own enduring cutting edge that made the difference.