Mandela saw the unifying possibilities of the triumph and attended the match and subsequent victory celebrations wearing a Springbok jersey. Rugby followers felt instantly that they belonged to the new South Africa.
"I have fought against white domination and I have fought against black domination. I have cherished the idea of a democratic and free society in which all persons live together in harmony and equal opportunity."
So said Nelson Mandela. Given what followed, the words could easily have heralded his release from jail in 1990. But he spoke them at his trial for sabotage in 1964. Twenty-seven years of incarceration would not dim his vision.
Once a shadowy figure whose imprisonment personified the shackles of his apartheid-bound people, a free Mandela brought political calm to a South Africa that had become far more savage since he was jailed.
The ending of his time as inmate No 46664 came as unrelenting violence increased fears that the unavoidable transition from white to black rule would be achieved in a sea of blood.
As with his release from jail, there was an inevitability about his country's release from apartheid. The 'how' was the issue. But both events took place with great dignity - a tribute to the man and to the people.
Much is still to be done. The township violence that was political in its resistance to (and manipulation by) white rulers later became criminal, growing from apartheid's legacy of poverty. But, again, Mandela epitomised his people's patience.
If they were not so patient, the slow progress in addressing their employment, housing, education and healthcare needs would have caused chaos by now. He was as much a son of his people as he was their father.
Commenting in 1985 on Mandela's imprisonment, Nobel Peace Prize winner Bishop Desmond Tutu said: "It may seem almost childish but the faith in him is so complete that somehow I think people believe that if he were to come out, things would be all right."
Not totally all right, but certainly much better than many expected.
Few revolutionary leaders can transform the ability to garner unswerving support into political effectiveness. Mandela could, and that may have been his greatest gift to his country. He used the legend that had developed around him to make the political transition peaceful beyond expectation.
Nelson Mandela could have led black South Africans anywhere. He led them on the route of peace, reconciliation and partnership, without the bitterness that would be understandable in normal mortals.
He did so by example. He gave his jailers a legitimacy they did not deserve. And while he embraced white leaders, notably President F.W. de Klerk, with whom he shared the 1993 Nobel Peace Prize, he kept the heat out of the militant blacks who would have preferred vengeance.
On being elected president in a landslide in South Africa's first all-race election in 1994, Mandela also eschewed quick fixes of the type pursued, for example, by Robert Mugabe.
His government adopted free-market policies that kept the white-dominated corporate sector on side and attracted foreign investment.
If progress in solving the country's many ailments has been pedestrian, there has certainly not been a Zimbabwe-like economic collapse.
New Zealand, if only obliquely, played its own part in Mandela's promotion of what became known internationally as the Rainbow Nation. The All Blacks were the beaten finalists in the 1995 World Cup, which was held in South Africa. Rugby had been a symbol of white, especially Afrikaner, power.
But Mandela saw the unifying possibilities of the triumph and attended the match and subsequent victory celebrations wearing a Springbok jersey. Rugby followers felt instantly that they belonged to the new South Africa.
The Free Mandela movement began in 1980. The West was suspicious because it was adopted by African states supported by Moscow in the Cold War battle for Africa and by left-wing European politicians and organisations. Getting a top Cuban award from Fidel Castro was also no way to improve Mandela's image in the West.
Yet a decade or so later, Western leaders were queuing to be photographed with the man dubbed in his renegade days the Black Pimpernel. One was a young United States senator named Barack Obama, who met Mandela only once, at a hastily arranged meeting in a Washington hotel room in 2005.
Yesterday, Obama - like Mandela his country's first black president - recounted how he drew inspiration from him. "Like so many around the globe, I cannot fully imagine my own life without the example that Nelson Mandela set."
Others, with full justification, placed him on a par with Martin Luther King and Mahatma Gandhi, both of whom also fought white rule, then sought peace with their enemies.
Those two men were assassinated. Mandela's years of struggle also took a heavy toll. Tuberculosis contracted in prison led to frequent hospitalisation for respiratory problems in the years before his death at 95.
Nelson Mandela showed the way. South Africans, in following him, have affirmed that his strengths are imbued in a united people. Now, the leaders left with the unenviable task of filling his shoes have a responsibility to honour his legacy.
Few transcend the aura that envelops their name. Nelson Mandela was one who did.