Steyn slotted over both of his three-pointers in the last 10 minutes after coming on as a substitute, the first a monstrous 45-metre kick from the sideline to level the scores after the hosts had trailed 16-19 with six minutes remaining.
And just two minutes from time the 20-year-old Sharks utility-back slotted the easiest of goals from 20 metres out, sending the 48,000 Newlands crowd into a frenzy as their team sealed what at times appeared an unlikely victory.
The Springboks started brightly and strung together a number of attacking phases in the opening 10 minutes, but only had a Percy Montgomery penalty to show for their efforts.
That score was cancelled out by the boot of Stirling Mortlock, but the Boks soon went over for the first try of the game.
A wave of attacks drew the opening, the hosts ultimately benefiting when Gurthro Steenkamp lost the ball in a tackle and Jaque Fourie charged through the gap to score in the corner.
Montgomery converted and the Boks were 10-3 up.
Mortlock then added a penalty to reduce the deficit before a controversial try fired Australia into the lead.
Referee Wayne Barnes incensed the hosts by allowing Matt Giteau's touchdown after Stephen Larkham had apparently obstructed Guy Shepherdson.
Mortlock added a another penalty to ease the Wallabies into a 16-10 lead at the break, and put over another shortly after the break to stretch the lead to nine points.
However, that was as good as it got for the visitors, and slowly and surely the Boks started to claw their way back into the game.
Montgomery hit penalties in the 46th and 53rd minutes but South Africa found the going difficult against a tough Australian defence.
That prompted a rethink from Boks coach Jake White, who introduced Steyn as a final throw of the dice that ultimately secured a thrilling triumph.