The Springboks last win over the All Blacks at Eden Park was 1937, and the last team to upset the hosts there was France in 1994.
The All Blacks have not lost a Test at home against any nation since John Smit's South Africa won 32-29 in Hamilton in 2009, a run of 28 successive victories that included their second World Cup title in 2011.
"There is a lot of confidence and belief that we can achieve something special," De Villiers said.
"I'm sure a lot of teams have come here in the past and felt the same.
"The reality of the matter is that the team we're playing tomorrow and the venue we're playing tomorrow, not many teams come away with wins.
"We will have to play better than we have ever played and have to make basically no mistakes and make sure the ball bounces in our direction."
South Africa demolished Australia 38-12 to win their first match at Lang Park after seven straight losses.
Based on a bruising forward display and three tries from the backline, the breakthrough in Brisbane was also their ninth Test win in succession.
Although pleased with their effort at Lang Park, De Villiers said their execution was wanting and he expected his side to raise that level against the All Blacks.
"It's massive for us. We want to be seeing constant improvement and I think maybe not so much on the scoreboard ... but the way we play," the 32-year-old said.
"We came off last week and on the scoreboard it was looking very good but from an execution point of view we could have been better.
"That's what we need tomorrow. We won't get many opportunities and we need to use the ones that we do get."
Recent history may be tilted against De Villiers' side, but the Springboks have traditionally been the All Blacks' greatest rivals.
The world champions' overall winning record is just under 76 per cent, and victory on Saturday would hand them a record 383rd win from 505 Tests, surpassing France's 382 from 695 matches.
Against South Africa, however, New Zealand's winning record is only 56 per cent from 85 Tests.
Both sides are unbeaten in the Rugby Championship, but the Springboks lead the table on 14 points, one ahead of the All Blacks. Some pundits rate the Eden Park game as the most important in New Zealand since the 2011 World Cup final.
De Villiers, who missed out on two World Cup tournaments due to injury, said he was feeling the expectations surrounding the Test, which will be his 90th.
"It is an All Blacks Test and that is always special," he said. "You can see all week that the All Blacks are excited for it as well. Everyone is looking forward to it.
"This would rank in the top three games I have played in.
"As a rugby player these are the games you look forward to."