So this is how it's done. Students in Quebec, in rebellion against their government over tuition fees, have scored an amazing victory in the province's general elections.

The Liberal government led by Jean Charest, which ran on a law-and-order platform against the students, has been defeated. Its plans to implement an 82% tuition fee increase are shredded for now, and the harsh emergency legislation it passed to quell the upsurge is history. Charest is resigning from politics. Two members of the leftist group, Québec Solidaire, have been elected, and the party gained more than 6% of the popular vote.

For those used to student movements that erupt suddenly only to deflate within a few weeks or months, this defies belief. How, then, was such an effective action actually sustained, in defiance of police crackdowns and emergency legislation?

Students in Quebec inhabit militant traditions inherited from the "quiet revolution" of the 1960s, when the province's francophone majority pushed for full access to higher education as part of a series of sweeping reforms. This inaugurated a student movement, whose signature was the mass student strike. Each time a government attempted to drive up tuition fees, the students walked out – and most of the time, they won. As a result, there is a thriving democratic culture among Quebec's students. While the NUS is converting itself into a tame lobbying organisation, Quebec students have a tradition of grassroots organising, and four relatively democratic federal organisations that rank-and-file student bodies can affiliate with.

The radical spearhead of the movement is the Coalition Large de l'Association pour une Solidarité Syndicale Étudiante, or Classe. Emerging from a decade of leftwing student unionism, Classe was explicitly formed in December 2011 to build a students' strike to stop the fees rise. Going further than most student bodies, it demanded the cancellation of all tuition fees, to be paid for by a tax on banks. This stance was very popular, and the group eventually incorporated 65 local affiliates and 100,000 members comprising the most politicised and activist core of the province's 400,000 strong student body.

General assemblies of students were held across Quebec, to discuss and implement a strike. This meant boycotting and picketing classes, and at their height the strikes achieved the support of 300,000 students. The structures of direct democracy built on campuses sustained the momentum behind the strikes, enabling students to meet, discuss and make decisions on a regular basis. Each month, the movement called a mass mobilisation, with tens of thousands of students gathering in the Place du Canada in Montreal. But there was also a heated debate over the strategy and goals of the movement. It wasn't enough to keep the momentum going. In addition to the strikes, radical students sought to disrupt the smooth functioning of the economy and the government, carrying out blockades and occupations of banks and government buildings.

But students also reached out to the labour movement. Theirs was a class issue, they insisted, and Classe called for a "social strike" of both students and workers. They consciously sought alliances with Rio Tinto workers locked out of their jobs, public sector workers facing cuts, campaigns against increased fees for healthcare, and local resistance to the government's attempts to turn over northern resources to the mining industry. Neighbourhood protests became a regular occurrence. A number of union federations passed motions for strike action, though as yet the resistance from union leaders is too strong, and the labour militants too weak, to make it happen.

Importantly, the student leadership refused to be divided. When the government excluded Classe from negotiations, in the hope of engaging the more moderate student federations in a compromise, the latter walked out.

The government's biggest mistake was passing Bill 78, imposing severe restrictions on the right of students to protest. Though supported by the Quebec Council of Employers, the bill was otherwise reviled. Rather than breaking the students, the repression produced a much wider movement. Up to half a million people marched in clear defiance of the law. Those returning home from law-breaking protests were greeted by families banging pots and pans in their support, from their windows and in the streets. Some of the country's largest trade unions joined in the protest. To get a sense of how improbable this is, compare it with our student protests beginning in November 2010, where the NUS and UCU leaderships organised timid demonstrations separate from the main protests.

The Liberals' defeat can be traced to that defiance. But the Parti Québécois, which has just won, is not an ally of the movement. The new government will probably seek to negotiate a smaller fees increase with the agreement of the less militant student bodies. At any rate, the movement has long been about more than fees. Classe intends to keep the pressure on, with new assemblies and protests, aiming to build the widest possible movement to challenge neoliberalism. British students should take the hint.

• This article was amended on 10 September 2012. It originally referred to Québec Solidaire as a student group. This has now been corrected.