White's team have now gone 14 games unbeaten at home since 2003 but have also lost 15 consecutive games on their travels against major rivals England, Australia and the All Blacks.
Travelling has never been a strength of Springbok sides but now with the world number two ranking secured, White is eager to change things.
"This team is used to meeting challenges," White said.
"No one thought we would beat Ireland at home last year and we did.
"We then had to win both our home Tri-Nations matches to win the title and we did. It's up to the guys to clear this next hurdle."
Springbok captain John Smit praised his players after the game, saying that the toss and the choice of playing with or against the wind, which was blustery on the day, counted in the home team's favour.
"We played into the wind in the first half, which worked out perfectly for us," said Smit.
"In the second half we had the wind behind us, which allowed our kickers to keep the All Blacks pinned deep in their own half.
"It was a crucial toss to win."
In contrast to the smiles of the Springboks, the All Blacks looked out of sorts, three weeks after whitewashing the British & Irish Lions.
"We were a bit rusty," All Black coach Graham Henry admitted.
"We didn't think we would be, but looking back we probably were. They took their chances, while we didn't take ours," he said.
"Their defence was outstanding and we failed to capitalise on our opportunities."
Henry believes the Boks have improved significantly since beating the All Blacks 40-26 at Ellis Park in the corresponding fixture last year.
"The Boks have more depth this year," he said. "There's a lot of competition for places, and that can only be good for a team. They've also grown as a team over the last year, as have we.
"[Saturday's] game was definitely a step up from the series against the Lions. The Boks are a team who are getting better and better."