You've got to hand it to English football. As superheated, financially-stupefied spectacles go, it can still pull off a grand sense of cup final occasion. On the face of it the story of Manchester City's triumph here in the Capital One Cup final – team spends inconceivable amounts of money: team wins minor domestic trophy – might look like another routine exercise in the overdog domination of English football's gold rush years. Just as in outline it might be hard to detect the romance in a disjointed but still somehow inevitable victory for a club not so much bankrolled as gullet-fed by the fossil fuel illuminati of Abu Dhabi. But then, this is a sport and a sporting culture that refuses to be suffocated. Days like these, for all the broader hierarchy of interests, are still about the fans, and City's boisterous, full-throated Wembley support celebrated here like an island full of shipwrecked men who have just spied a sail on the horizon.

City were always likely to win this final, the cutting edge in that stellar attacking midfield just too much even in a patchy performance against opponents who were for long periods the better team. And yet despite the sense of inevitability about the result this was still a brilliantly entertaining final, an occasion memorable for the sense of unaffected excitement among both sets of fans.

Football has done its best to suck the joy out of these occasions both in terms of staging and broader priorities. But as Vincent Kompany lifted the trophy to the strains of a wretchedly intrusive PA system, the air filled with sky blue streamers in a further nod to the usual nannied euphoria, there was still something unbound and gloriously incredulous in the reaction of City's fans and players who, for all their pedigree, honoured this competition by giving everything on the pitch and celebrating wildly in victory.

It seems safe to say City's owners have not invested £1bn in the club's redevelopment in order to see their team edge past Sunderland on a drizzly afternoon in early March. Given the choice the club's hierarchy would no doubt swap a cup win here for victory in the Champions League last-16 tie against Barcelona and the promise of a more worldly kind of progress. Not City's fans, though, for whom, as for all supporters, football is a game marked out by moments such as these, and for whom this was a day of almost rather subversive old-school glory.

Hours before kick-off Wembley had been transformed into a crush of fevered blue, red and white. Such is the magic of the cup, any cup, even one subjected as here to a slightly bizarre pre-match routine featuring giant flag-carrying zeppelins – "Ladeeezzz and gentleman pleazzz show your appreciation for … your club's crest!" – and a strange interlude with a floating spandex-clad gymnast performing an overwrought modern dance routine with the trophy itself, as though overcome by its wondrous mystical powers. Have a little faith, Wembley, you felt like saying. It's football. We're already excited.

As the match kicked off to an ear-tingling crackle of noise around this refurbished steel and concrete megadome Lee Cattermole and Jack Colback set about the task of stifling City's midfield, which they did with some success. In fact Sunderland were excellent throughout, with Cattermole, Colback and Ki Sung-yueng uncowed in midfield against a dauntingly strong City team.

Sunderland's opening goal after 10 minutes was exhilarating, Fabio Borini's finish with the outside of his right foot a superbly executed moment of craft. And so the match settled into an unexpected rhythm of energetic Sunderland pressing and some strangely meandering City possession, matched in the Wembley stands by a peculiar sense of foreboding among their supporters.

On the touchline Manuel Pellegrini mooched and pointed vaguely, while Gus Poyet was his usual frantic air-throttling self, a man who has to fold his arms across his chest simply to stop them jangling about like the wings of a particularly agitated carved wooden woodpecker.

And yet football is a game where enough thickly ladled talent will always make the difference. Yaya Touré had barely figured in the opening 55 minutes but it took a single perfectly calibrated swing of his right foot to alter completely the gravity of this match, the ball dipping perfectly into the far top corner. Moments later a goal kick, three touches by Sergio Agüero, a cross from Aleksandar Kolarov and Samir Nasri had sent the ball whiffling first time into the far corner. And suddenly the stadium had been tipped on its side, the noise and ceaseless movement of the red half now sloshed down decisively into the blue end as victory was capped by Jesús Navas's late third goal.

Afterwards Pellegrini, for whom this was a first piece of silverware since Intertoto Cup glory with Villarreal in 2004, was his usual inscrutable self, confirming his belief above all in the wider project and all the rest of it. Somehow it wasn't quite the moment for that. For all the broader textural changes in English football, you really can't – try as you might – kill the spirit, and this felt like a significant moment both for City's fans who saw their team win this trophy for the first time since 1976, and for the broader sense of undampened life in a genuinely stirring domestic occasion.