It was the night Manchester City made it clear they have no intentions of relinquishing their grip, finger by finger, on the Premier League trophy.

Pep Guardiola and his players will cling to the belief that this victory could be a decisive blow and, at the very least, it has clipped back Liverpool when they were threatening to pull away.

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If City were to prolong the argument, it was imperative they found a way past the leaders. Even a draw would have felt like a grievous setback for the reigning champions and, when Roberto Firmino nodded in Liverpool’s equaliser, approaching the midway point of the second half, a lesser side than City could conceivably have wilted under the pressure.

Not this team, though. As the song goes, City fight to the end and it was not just their competitive courage to conjure up a decisive goal, courtesy of Leroy Sané, that delivered a message. It was the spirit of togetherness displayed by Guardiola’s players in that nerve-shredding finale when Liverpool started pumping balls into the penalty area.

On one hand City have not kept a clean sheet during their past 11 fixtures. On the other it was a show of collective defiance during those fraught moments when Liverpool had Virgil van Dijk operating as an extra centre-forward. City gave everything to defend their lead, in the way that true champions do. They dug in, they formed an impenetrable blue line and, when it needed the ugly stuff, they were happy to oblige. In the process they made it clear to their opponents it is going to be one hell of a battle between now and the end of the season.

Facebook Twitter Pinterest Sergio Agüero celebrates rifling in the opening goal from an acute angle. Photograph: Peter Powell/EPA

For Liverpool the priority must be not to wallow in self-pity. It is, after all, only a month ago that City were five points clear and looking capable of turning the title race into a procession. Liverpool still have a four-point cushion and, if they need encouragement, there is only one other club in history who has reached the new year unbeaten and not gone on to win the league – and that was Sheffield United in the 1899-1900 season.

Liverpool will, however, reflect that the night could have taken a very different complexion but for an astonishing goalline clearance from John Stones. And Jürgen Klopp should be aggrieved that, having made it 1-1, his players left themselves so stretched when Sané collected Raheem Sterling’s pass and fizzed a diagonal shot past Alisson to score via the far post.

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Perhaps Liverpool might have been better to employ more restraint once Andrew Robertson, the game’s outstanding performer, had turned Trent Alexander-Arnold’s long cross into the six-yard box for Firmino to equalise with a stooping header. It is difficult to be too critical after such an absorbing game but Liverpool lost their shape at the key moment and Sané punished them with a brilliantly angled finish.

Klopp also made the point that, with the game goal-less, Vincent Kompany was fortunate to be shown only a yellow card for a scything challenge on Mohamed Salah.

City certainly rode their luck at times and never more so than when Salah played Sadio Mané through the middle, the shot thudded off the post and for a split-second, as Stones’s first attempt to clear the danger came back off Ederson and started looping towards an exposed net it felt as if the entire stadium held its breath, anticipating an own goal.

The technology showed nine-tenths of the ball had crossed the goal-line – but not the final tenth. Stones had somehow got back to hook the ball away, brilliantly, from beneath his crossbar and City were spared by a matter of millimetres.

Facebook Twitter Pinterest John Stones clears the ball off the line to prevent a farcical own goal giving Liverpool the lead. Photograph: Shaun Botterill/Getty Images

When Liverpool watch the replays they will barely comprehend how Stones’s final swing of the ball missed Salah, from point-blank range, when even the merest of touches would have resulted in a goal.

City made the most of their fortune and, when Sergio Agüero put them into the lead, five minutes before half-time, it was a reminder that the truly great strikers tend to save their best for the big occasions.

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Bernardo Silva did the build-up work on the left and for the first time Agüero had manoeuvred a yard for himself inside the penalty area. He was still left with an acute angle, shooting left to right, with an outstanding goalkeeper to beat in the shape of Alisson. Agüero had nicked the ball in front of Dejan Lovren but still had his opponent in close proximity.

It was the kind of shooting opportunity, on the half-turn, that many strikers would have passed up, concluding that the chances of scoring were too remote. His finish was a beauty – swivelling on the spot and connecting with power and precision. The ball was still rising as it soared between Alisson and his near post and City had the breakthrough they craved.

That goal continued Agüero’s record of having scored on all seven occasions he has faced Liverpool in league fixtures at this stadium. More importantly, it gave the home team an element of control when, until that point, Liverpool had seldom looked in trouble. Robertson had been coping with Sterling, Alexander-Arnold had the speed and agility to match Sané and, until that piece of brilliance from Agüero, it was unusual to see City finding it so difficult to create chances.

Equally, the same could be said of Liverpool for most of the game and, if City’s supporters had any apprehension about seeing Danilo and Aymeric Laporte operating as their team’s full-backs, it was gone by the end.

Liverpool’s 20-match unbeaten run was over and, for City, the title race had opened up with new possibilities.