When it comes to seeking inspiration for football terrace anthems, the 1970s melodies of the Carpenters are not an obvious option. But late into the evening on bonfire night in Rochdale, thousands of beery Mancunian voices were channelling sunny Californian optimism into the damp Lancashire air:

"I'm on the top of the world," they sang, "looking down on creation, and the only explanation I can find, is the love that I've found ever since you've been around. Your love's put me at the top of the world."

The song is the latest favourite of the supporters of FC United of Manchester, the rebel club formed five years ago in opposition to the debt-laden takeover of Manchester United by the American Glazer family. And this weekend the lyrics just about sum the situation up.

I became a founder member of FC United in the summer of 2005, but never expected to witness scenes such as those at Rochdale AFC's stadium on Friday night, when FC United won 3-2. A non-league club conceived by a few angry dreamers in a Manchester curry house reached the second round of the FA Cup, beating a team four leagues above it with a winning goal in the last minute of injury time.

Bedlam, hysteria, delirium: no word can do justice to the scenes that followed. Jerome Wright, the club's cult forward, was still being chaired half-naked around the pitch half an hour later.

For many of the 4,000 FC fans who were wiping their eyes or locked in embrace with total strangers, a big away game used to mean Milan or Barcelona, following Manchester United. They still sing the name of Eric Cantona, the French forward and United hero, who has gone on record to support their anti-Glazer stance.

But somehow, for many of them, Rochdale was bigger than Milan. One fan said before the game that he had not looked forward to a game so much since Manchester United played in the European Cup final in 1999.

There were tears, flares, flags and endlessly swirling green and gold retro scarves. And at the final whistle there was sheer incredulity at the fact that something no one in the 7,000-plus crowd thought could happen actually had happened. "That was simply unreal," said Adam Brown, a member of the board of directors.

It was a night that gave sublime, heady vindication to a rebellion without precedent in the history of football. At the time of FC's formation, in the bleak aftermath of the takeover, there was a recurring image that summed up the attitude of a protest movement that wanted to do more than just oppose.

Back then the archetypal FC rebel would listen politely to all the pundits, Premier League officials and financial experts, nodding dutifully when told that the new Glazer regime, high ticket prices and outlandish salaries for players were just "part of modern football".

Then he or she would say: "Sod that. We'll do it this way."

FC are fan-owned. Each of the members has a vote on all important matters. Tickets are kept inexpensive. A commitment to community work is written into the club's constitution.

Manchester city council has been so impressed with the activities organised by the club in some of the most deprived areas of the city that it is expected to grant FC a lease to build their own ground in Newton Heath – where what was to become Manchester United was founded by railway workers in 1878.

More than 300 of the club's members volunteer in vital tasks to help keep the costs down. If David Cameron wants a vision of the "big society" in action, he can find it at FC.

The players play not for the money, but for the adulation of some of the biggest crowds in non-league football. The club's star striker, Michael Norton – scorer of the winning goal on Friday night – earns £80 a week playing for FC, almost £200,000 a week less than Wayne Rooney.

One much-loved ex-player, Rob Nugent – a big Manchester United fan – has just been voted on to FC's board. In his introductory statement to members, he wrote: "I retired from playing football after qualifying as an accountant, but still want to be involved with a club that I have supported since the first meeting. I have already been assisting the board with the management accounts, and would like to use the skills I have gained professionally in this manner and show that there is another way for football clubs to be run."

All this passion has found joyous expression in a set of supporters who are perhaps the loudest, most colourful and irreverent in English football. The banners and flags on display at Rochdale – and every week at the club's current home in Bury – are a triumph of attitude and chutzpah. "MUFC – FCUM – I've got love enough for two" reads one, reflecting the fact that almost all FC fans remain attached to their first love, Manchester United.

"A Right Bunch of Dicks" states another, in happy acknowledgement that not everyone has welcomed the FC revolution. Certainly not the Manchester United manager, Sir Alex Ferguson, who once described the club's fans as "self-publicists".

The songs are upbeat and defiant, ranging from the Carpenters cover to an FC reworking of the Sex Pistols' lyric "I am an anarchist" ("I am an FC fan"). Another favourite, "He sells asparagus", celebrates manager Karl Marginson's past as a fruit 'n' veg delivery man.

Friday night's triumph at Rochdale, which was shown live on television, announced FC United of Manchester to the wider world. In that packed, rocking stand, where the level of support would not have disgraced the Nou Camp in Barcelona or the San Siro in Milan, it felt as if we were attending a political rally and a raucous religious service, as much as a football match.

The money from this scarcely believable cup run – ESPN paid FC £67,000 for the right to screen the Rochdale match – will go towards building the club's own ground. The publicity will build the profile of a club that is already taking on a special charisma of its own.

An extraordinary thing has happened. Out of the bitterness, division and recriminations that surrounded the debt-fuelled takeover of England's most charismatic football club by a Florida businessman, a new club has been born. Bring on the second round.