But it almost went wrong on the day in Finland.
Williams topped the 33 qualifiers with a leap of 6.16m. Her closest rival, Aleksandra Chudina of the Soviet Union, managed 5.77m. The stage was set.
Williams, off her 33-metre runup, had two no jumps. Gathered around wirelesses the length and breadth of the country in the middle of a winter's night, New Zealanders held their breath. The field was to be whittled down to six, and Williams had one chance to make it.
She sprinted, leaped, and a white flag was raised by the official, indicating a fair jump. It was 5.94m, good enough to get her into the final.
Her fourth jump was perfect, and an Olympic record, half an inch off the world mark.
Chudina couldn't match it. None of the other finalists came close, and Williams had the gold.
Haka broke out in the stands, suggesting some things don't change half a century on, rain poured but no one cared.
The medals were presented by Arthur Porritt, bronze medallist in the 100m at Paris, who had been team captain when Ted Morgan won New Zealand's first Olympic gold, and manager and mentor when Jack Lovelock won his in 1936.
A telegram arrived for Williams: "Congratulations Chickie. Wonderful effort. Mighty proud of you. Dad."
Williams was sixth in the shot put and 10th in the discus, demonstrating her remarkable versatility.
She set a world record of 6.28m in the long jump at Gisborne two years later, played basketball for New Zealand and was Otago's named Sportsperson of the Century in 2000.
Her place among New Zealand's sporting greats is secure.