The transformation of Latin America is one of the decisive changes reshaping the global order. The tide of progressive change that has swept the region over the last decade has brought a string of elected socialist and social-democratic governments to office that have redistributed wealth and power, rejected western neoliberal orthodoxy, and challenged imperial domination. In the process they have started to build the first truly independent South America for 500 years and demonstrated to the rest of the world that there are, after all, economic and social alternatives in the 21st century.

Central to that process has been Hugo Chávez and his Bolivarian revolution in Venezuela. It is Venezuela, sitting on the world's largest proven oil reserves, that has spearheaded the movement of radical change across Latin America and underwritten the regional integration that is key to its renaissance. By doing so, the endlessly vilified Venezuelan leader has earned the enmity of the US and its camp followers, as well as the social and racial elites that have called the shots in Latin America for hundreds of years.

So Chávez's remarkable presidential election victory on Sunday – in which he won 55% of the vote on an 81% turnout after 14 years in power – has a significance far beyond Venezuela, or even Latin America. The stakes were enormous: if his oligarch challenger Henrique Capriles had won, not only would the revolution have come to a juddering halt, triggering privatisations and the axing of social programmes. So would its essential support for continental integration, mass sponsorship of Cuban doctors across the hemisphere – as well as Chávez's plans to reduce oil dependence on the US market.

Western and Latin American media and corporate elites had convinced themselves that they were at last in with a shout, that this election was "too close to call", or even that a failing Venezuelan president, weakened by cancer, would at last be rejected by his own people. Outgoing World Bank president Robert Zoellick crowed that Chávez's days were "numbered", while Barclays let its excitement run away with itself by calling the election for Capriles.

It's all of a piece with the endlessly recycled Orwellian canard that Chávez is some kind of a dictator and Venezuela a tyranny where elections are rigged and the media muzzled and prostrate. But as opposition leaders concede, Venezuela is by any rational standards a democracy, with exceptionally high levels of participation, its electoral process more fraud-proof than those in Britain or the US, and its media dominated by a vituperatively anti-government private sector. In reality, the greatest threat to Venezuelan democracy came in the form of the abortive US-backed coup of 2002.

Even senior western diplomats in Caracas roll their eyes at the absurdity of the anti-Chávez propaganda in the western media. And in the queues outside polling stations on Sunday, in the opposition stronghold of San Cristóbal near the Colombian border, Capriles voters told me: "This is a democracy." Several claimed that if Chávez won, it wouldn't be because of manipulation of the voting system but the "laziness" and "greed" of their fellow Venezuelans – by which they seemed to mean the appeal of government social programmes.

Which gets to the heart of the reason so many got the Venezuelan election wrong. Despite claims that Latin America's progressive tide is exhausted, leftwing and centre-left governments continue to be re-elected – from Ecuador to Brazil and Bolivia to Argentina – because they have reduced poverty and inequality and taken control of energy resources to benefit the excluded majority.

That is what Chávez has been able to do on a grander scale, using Venezuela's oil income and publicly owned enterprises to slash poverty by half and extreme poverty by 70%, massively expanding access to health and education, sharply boosting the minimum wage and pension provision, halving unemployment, and giving slum communities direct control over social programmes.

To visit any rally or polling station during the election campaign was to be left in no doubt as to who Chávez represents: the poor, the non-white, the young, the disabled – in other words, the dispossessed majority who have again returned him to power. Euphoria at the result among the poor was palpable: in the foothills of the Andes on Monday groups of red-shirted hillside farmers chanted and waved flags at any passerby.

Of course there is also no shortage of government failures and weaknesses which the opposition was able to target: from runaway violent crime to corruption, lack of delivery and economic diversification, and over-dependence on one man's charismatic leadership. And the US-financed opposition campaign was a much more sophisticated affair than in the past. Capriles presented himself as "centre-left", despite his hard right background, and promised to maintain some Chavista social programmes.

But even so, the Venezuelan president ended up almost 11 points ahead. And the opposition's attempt to triangulate to the left only underlines the success of Chávez in changing Venezuela's society and political terms of trade. He has shown himself to be the most electorally successful radical left leader in history. His re-election now gives him the chance to ensure Venezuela's transformation is deep enough to survive him, to overcome the administration's failures and help entrench the process of change across the continent.

Venezuela's revolution doesn't offer a political model that can be directly transplanted elsewhere, not least because oil revenues allow it to target resources on the poor without seriously attacking the interests of the wealthy. But its innovative social programmes, experiments in direct democracy and success in bringing resources under public control offer lessons to anyone interested in social justice and new forms of socialist politics in the rest of the world.

For all their problems and weaknesses, Venezuela and its Latin American allies have demonstrated that it's no longer necessary to accept a failed economic model, as many social democrats in Europe still do. They have shown it's possible to be both genuinely progressive and popular. Cynicism and media-fuelled ignorance have prevented many who would naturally identify with Latin America's transformation from recognising its significance. But Chávez's re-election has now ensured that the process will continue – and that the space for 21st-century alternatives will grow.

@SeumasMilne