Unable to lose the series, the team went on win the third test before drawing the last, earning themselves the famous tag of the Invincibles and ensure they would go down in history.
On the score sheet alongside Williams in Pretoria that day were Richard Milliken, Gordon Brown and Phil Bennett, with the latter's marauding run starting a fine team move.
"I can remember the pitch was rock hard," recalled Bennett. "They were playing very well and I remember the kick going deep inside the 22 near our own line, grabbing the ball, beating the first man and thinking hang on, there's something on here."
Driven on by Bennett, the ball was switched throughout the side several times before Roger Uttley's superb footballing skill kept the move alive on the byline leaving Williams to gobble up for the try.
His double made him the first Lions in the 20th century to score two tries in a test, as the tourists further proved their credentials as the team to beat.
Williams' other try came with the help of the boot of scrum-half Gareth Edwards and the former Welsh international believes the performance firmly put to bed those questioning whether they could maintain their form in the high veldt.
"You had quite outstanding players then, and quite outstanding players not even being able to make the test side," he said.
"The side was full of great individuals and experienced players who knew we had the basis of a good side, but who knew also it would take more than that to beat the Springboks.
"The Lions played some outstanding rugby in that game, highlight by some outstanding tries from certain individuals. JJ Williams chasing a long kick over the top from myself.
"Then there was Phil Bennett scurrying and darting and side stepping to score the most dramatic of tries.
"Maybe one which gave me a certain satisfaction, a wonderful try from the late Gordon Brown when he came up on the inside and I'm not sure if he shouted at me in Welsh but it seemed very like it to pass inside when he scored in the second half to make the match secure for the Lions
"It was quite an outstanding performance experience to win so comprehensively in the high veldt."