The two teams are third and fourth respectively in Group A, after hosts Bafana Bafana played an opening stalemate against Iraq while the Kiwis lost 5-0 to Spain.
Despite the heavy defeat at the hands of Vicente Del Bosque's men, New Zealand coach Ricki Herbert and his players believe South Africa will be the team under pressure.
"South Africa will be looking to win after Iraq and will be under a lot of pressure," Herbert said.
"We are looking for our first point, and we have a chance to get it tomorrow."
New Zealand skipper Tim Brown agrees with Herbert that his team will have the advantage of playing without any stress.
"Hopefully we can turn around after the Spanish game and create history by causing an upset," Brown said.
"We're not under any pressure, we can play with freedom, perhaps unlike South Africa."
South Africa's Reputation
After the country's failure to secure qualification to the 2010 African Cup of Nations, coach Joel Santana is now fighting to save both his and the country's reputation.
The Brazilian tactician believes that the tough task ahead of his team needs his players to be more relaxed.
"We need four or five points for the semi-finals and that's what we're aiming at. We have to be less nervous," Santana stressed.
Everton's Steven Pienaar, who regained full fitness, is set to start for South Africa after only coming on as a substitute against Iraq.
Skipper Aaron Mokoena will also lead his team despite a minor shin problem he sustained against Iraq.
New Zealand defender Ben Sigmund recovered from a hip injury and might be recalled for the game.