Smith said after the 30-22 win at Cape Town, the Springboks are determined to take on their 88-year Eden Park drought.
"It's a massive game, going to Eden Park. Even when we lost the other game in Auckland a few years back, I was disappointed we didn't play well.
"It's going to be a tough game—New Zealand's obviously a great opponent.
"But for us, it's trying to get better every game and taking that confidence and learning from every game we play to get better."
South Africa were under pressure to lift their game after their shock opening round loss to Australia at Ellis Park.
"It was very important for us to get the win, but at the same time, we learnt from the previous match; we knew what we had to fix. If you don't learn and lose, then you're in a bit of trouble.
"You also learn the most from losing; if you just keep winning then sometimes you tend to brush small things off and carry on. When you lose reality hits hard and you need to make sure you learn from your mistakes."
South Africa has been boosted ahead of its two-Test trip to New Zealand with Siya Kolisi, Pieter-Steph du Toit, Jan-Hendrik Wessels and Willie le Roux all returning from injuries.
Coach Rassie Erasmus said, "This group has been working hard since our first training camp in June, and most of them have been playing together for years, while the newer players in the squad have shown that they are ready for this challenge."
South Africa's win over Australia has lifted them back into No2 in World Rugby's rankings and closing in on the All Blacks who are only 0.71 ahead after their loss to Argentina.
Find out where to watch the Lipovitan-D Rugby Championship around the world HERE.
Click HERE to play Fantasy Rugby Championship.