Their commanding officer, Lieutenant Colonel Pienaar, later justified the use of pre-emptive force with a potted version of the white supremacist social darwinism underpinning apartheid: "The native mentality does not allow them to gather for a peaceful demonstration," he said. "For them, to gather means violence."
In what became known as the Sharpeville Massacre, 69 demonstrators were killed and 180 wounded. Many were shot in the back as they tried to flee.
The United Nations Security Council condemned the massacre and called upon the white minority Government to abandon apartheid, thereby setting in motion the campaign to make South Africa a pariah state. The South African Government responded by imposing a state of emergency, banning the main black political organisations, the African National Congress and the Pan-Africanist Congress, and imprisoning many of their leaders, including Mandela, without trial.
Less than two months later, an all-white All Black team began a 26-match tour of South Africa. Anxious not to offend its Afrikaner hosts and indifferent to the views of the 150,000 Kiwis who signed a "No Maoris, No Tour" petition, the New Zealand Rugby Union (NZRU) had maintained its policy of not considering Maori players for tours of South Africa.
The test series was lost 2-1, with one match drawn. The All Blacks had failed, yet again, in their quest to win a series in South Africa; the Springboks were still ahead in the overall win/loss comparison; and New Zealand rugby's already unhealthy obsession with its rival was about to take a turn for the worse.
In 1961, Mandela was acquitted of treason after a six-year trial. The following year, he was charged with four counts of sabotage and conspiring to overthrow the Government. Although he dodged the death penalty, he was sentenced to life imprisonment and incarcerated in a 2.4m by 2.1m damp concrete cell on Robben Island.
While Mandela languished in prison for 27 years, South Africa receded further and further into isolation while New Zealand became increasingly divided over the sporting contacts issue. Eventually the South African infection in our body politic brought the nation to fever pitch.
The Springboks' 1965 tour of this country was incident-free; in retrospect the calm before the storm. But as the tour was winding up, South African Prime Minister Hendrik Verwoerd declared that the NZRU would have to continue the obliging practice of omitting Maori from its touring squads. Bowing to public opinion the NZRU advised its South African counterpart that this was no longer possible, thereby triggering the cancellation of the 1967 All Black tour.
But South African rugby folk were no less desperate to preserve the relationship, equal parts intense rivalry and mutual dependency. After Verwoerd's successor John Vorster softened the stance, Maori and Pacific Island All Blacks such as Sid Going and Bryan Williams were classified as "honorary whites" to enable them to take part in the rescheduled tour in 1970.
When Norman Kirk's Labour Government forced the cancellation of the 1973 Springbok tour, Kiwis who had previously been on opposing sides of an admittedly vigorous argument suddenly found themselves poles apart. The issue suited Robert Muldoon's combative personality and populist instincts.
Having exploited it to win power in 1975, he was never going to back down in the face of African nations' threats of retribution if the All Blacks went ahead with their proposed South African tour the following year.
On June 16, 1976, a black student protest against being taught in Afrikaans - "the language of the oppressor", as Desmond Tutu called it - snowballed into the Soweto uprising. When the state had finished teaching the recalcitrant children a lesson, 176 of them were dead - although some estimates put the death toll as high as 700 - and more than 1,000 were wounded.
Two weeks later, the All Blacks kicked off their 24-match tour of the republic. The test series was lost 3-1 and 25 African nations boycotted the Montreal Olympics in protest at New Zealand's presence.
The fallout - a "diplomatic disaster unprecedented in the country's history", according to historian Malcolm McKinnon - persuaded Muldoon to sign the 1977 Gleneagles Agreement, which committed the parties to discouraging sporting contacts with South Africa.
For the other signatories, "discourage" meant using the powers of the state - passport confiscation, refusal to grant visas - to stop their athletes going to South Africa and its athletes setting foot on their soil. Typically, Muldoon chose to interpret it rather differently. His "discouragement" of the 1981 Springbok tour of this country was probably the only time in his political career when he could have been accused of diffidence.
The 1981 tour was the dead end of the cul-de-sac down which New Zealand had been dragged by a section of the community obsessed by the All Black-Springbok rivalry and insistent that sport could and should quarantine itself from the wider world, even when that meant turning a blind eye to a system that had elevated racism into a state ideology and legalised political, social and economic discrimination.
It was a catastrophic bookend to the torrent of international condemnation that followed the 1976 tour. As Prime Minister Jim Bolger said 15 years later, "The tour reached into - and often divided - families, friends and communities throughout New Zealand, perhaps more than anything in our recent history."
Like Monty Python's absurd Black Knight who continues to bellow defiance despite being shorn of his limbs ("Tis but a scratch!"), there were still diehards who refused to accept that the game was up. In 1986, most of the All Black squad were induced to slink off to South Africa behind the NZRU's back. They claimed to be striking a blow for freedom, a well-rewarded one as it turned out, but most Kiwis were appalled at the damage done in that spurious cause and sick of swimming against the tide of history. The Cavaliers were dismissed as mercenaries, an appropriate tag, for what were they if not guns for hire in mock uniforms shoring up a beleaguered and discredited regime?
In 1989, the Berlin Wall came down, thus denying the apartheid regime its last claim on Western support, that of being a bulwark against communism. The wind of change that British Prime Minister Harold Macmillan had detected blowing through Africa in 1960 had become a hurricane.
Mandela had rejected several offers of release because they came with strings attached. In February 1990, the offer was made unconditional and he left prison to keep his date with destiny by becoming the first leader of a democratic South Africa.
He may have forgiven New Zealanders for their long dalliance with the oppressor, but you can't help but think that he savoured his role in the Springboks' victory in the 1995 World Cup final.
His appearance in a Springbok jersey was first and foremost an artful PR gesture intended to disarm suspicious Afrikaners and unite the fledgling democracy, but surely part of him relished the opportunity to inspire yet another haunting All Black defeat on South African soil.
Perhaps he also appreciated the irony of a black leader who had been labelled a terrorist by the apartheid regime walking out on to Ellis Park, that temple of Afrikanerdom, in a Springbok jersey with number 6 on the back, as worn by the Rainbow Nation's captain, a flaxen-haired Afrikaner named Pienaar.
And amid the drama, there was a little karma. The All Black manager was a member of the 1960 and 1970 touring sides, a tireless advocate of "bridge building" who hadn't let the fact that he was an NZRU-appointed All Black selector stop him coaching the Cavaliers, an iconic figure regarded by many as our greatest All Black: Colin (now Sir Colin) Meads.
• Read the full coverage on Nelson Mandela.
