The best moment of this game came 13 minutes from time, and will almost certainly be forgotten to history. Savinho brings down John Stones’s long ball with his chest and lashes the ball home, and of course this is the part that matters: Manchester City 3-1 up and safe at last. There is no Fifa Best award for “Greatest Chest Control of the Year”. But there should be.

It was, quite simply, one of the great chest touches. The perfect spot on the breastbone: not too much rib, not too much nipple. Just the right amount of give in the torso to send it forwards, not up or down: the ball not so much cushioned as sprung. Because now the ball is sitting up beautifully, and Simon Mignolet can probably do better at his near post but that’s hardly the first time we’ve said that.

Related: Guardiola says Manchester City are not yet capable of Champions League glory

And so City qualify for the next stage of the Champions League. Hold the presses. Could have predicted that five months ago, Nostradamus. But of course the “what” is much less interesting than the “how” and, on an unbearably taut night at the Etihad Stadium, City ended their group stage largely as they lived it: in a blur of half-sensations, a night of wild mood swings and inexplicable random fire.

Not until Savinho’s goal, 707 minutes into their Champions League campaign, could City truly relax. Was there really not an easier way of doing this? Perhaps, but then you would also struggle to match the thrill and the catharsis of the moment itself: a goal of pure haptics, a goal that felt fresh and interesting, a new way of getting to a familiar place.

And perhaps this has been true of City themselves over recent weeks, a club working through some strange feelings: jaded and defiant all at once, utterly fixed on their target and yet staggering towards it, lapsing in and out of focus like a camera on the blink. A few months ago City were losing convincingly. Now they’re winning unconvincingly, which is obviously preferable but still raises a few questions.

Above all there is a kind of madness behind the eyes here, most evident when the camera pans to Pep Guardiola and the Catalan is invariably doing something entirely devoid of context: pressing his fingers into his eyeballs, making forked lizard tongues at the fourth official, kicking a drinks crate to destruction, laughing uncontrollably at a joke only he really appears to understand.

And yet, if it’s often hard to work out what City are trying to do these days, their opponents came with a plan of perfect clarity. Brugge are through on merit, totally resolute off the ball, totally committed on it. Nicky Hayen’s side were determined to pass their way out of any trouble, actively tried to bait the City press, drawing them in before slicing the ball in behind.

After a bright start, the game settled into a familiar pattern: lots of sterile City passing and quarter‑chances around the edges of two solid Brugge banks of five. The Etihad Stadium was eerily quiet: less do-or-die Champions League showdown and more one of those Victorian science lectures when huge crowds would gather in respectful silence to watch a man in a tailcoat very slowly examining fossils.

The first shot on target went to Brugge, and so did the opening goal. Matheus Nunes has been shoehorned into right-back in recent weeks and plays like a man with distinctly mixed feelings about this turn of events. Here he lunged at Ferran Jutgla and took only thin air, allowing Jutgla to cross for Raphael Onyedika to score.

So. Which of your champion players steps forward in this moment of crisis? Not Ilkay Gündogan, who went off at half-time. And not Kevin De Bruyne, who still looks a little short of zip. Not really Erling Haaland, who was tidy without ever really threatening. Instead it was Savinho, City’s youngest player on the pitch, who came on at the break and offered the clean straight lines that they were craving.

With Savinho hugging the left touchline and drawing defenders with him, spaces began to open in the centre. Eight minutes into the second half Mateo Kovacic, who had been gradually nudging his way into the game, took the ball out of the centre circle and simply ran straight for goal. Then a neat Savinho pass to Josko Gvardiol produced an own goal. And finally the flourish: the chest of the century, the chest heard around the world.

Weird campaign, really. City scored more goals than table‑toppers Liverpool while finishing 21 places below them. Led in six of their eight games but somehow managed to win only three of them. And yet they’re still here, still hungry, still a little mad behind the eyes, but still possessed by enough crazy genius to get them through the tough moments. This season has been a wacky adventure. But it may just end up in a familiar place.