Captain Siya Kolisi told media ahead of the keenly-awaited game that, "The rivalry is the best it's been in a while, so I'm looking forward to the game.
"We will give them the respect they deserve, but all that we can do and sort out is obviously ourselves. We are in a good place at the moment.
"They were quite dominant before the past two years, and then we had to fight back as a team to make sure that we got a little of the respect back," he said.
Kolisi wouldn't say whether the Springboks felt they had a mental edge over the All Blacks after snatching a last-minute 16-16 draw in Wellington this year.
"I wouldn't know…I'm not in the changing room. I wasn't there physically in Wellington, but I could see how the guys were.
"It has been close and we can't say who will have an edge over whom as it's been one point, two points, and then we played to a draw in the last one.
"That's why this game is really important, to see where we are as a group. You never know, after this, we might meet them again. So, it's a really big game, and I wouldn't say we have the edge or they have the edge – it's 50-50 at the moment."
But he did say the Yokohama contest would be a yardstick on whether the balance had shifted.
"We work really hard and the only way we could see whether we are improving or not is to test yourself against the best in the world," he said.
They had taken a lot of belief from their 36-34 Rugby Championship win in Wellington in 2018 and hadn't looked back since then.
"We just believe we can get better and better. That's what we strive for. They are tough opposition to test yourself against, but you can see where you are when you play against them.
"We have been doing the training, and that keeps the nerves out – just being able to focus on our jobs. That is how I have been able to not think too much about the game," he said.