It has been almost 10 years since South Africa beat Nigeria and that friendly triumph in November 2004 was their only success against them in nine attempts.
However, the hosts are in a confident mood after coach Shakes Mashaba's new-look side comfortably beat Sudan 3-0 to begin their AFCON qualifying campaign with a win on Friday.
Defending champions Nigeria, meanwhile, succumbed to a shock 3-2 defeat at home to Congo on Saturday.
And South Africa captain Meyiwa believes his side are primed to heap more misery on Wednesday's visitors to Cape Town, ending a long wait for a victory over Nigeria in the process.
"Yes, they say in soccer certain teams have their hoodoo side but we are ready for the Nigeria match," Meyiwa said. "We are all determined to change the course of history and everyone cannot wait for Wednesday.
"The fact that they lost to Congo has not affected our preparations and determination; we are just concentrating on our task at hand and that is to beat them at Cape Town Stadium on Wednesday."
Mashaba also believes that his charges have what it takes to make it two wins from two in qualifying.
"We are meeting our nemesis but my gut feel is that all that is about to change. Wednesday should be a defining moment," he said.
Nigeria coach Stephen Keshi played down Saturday's loss to Congo and called for support from the media and fans to help them achieve a result in South Africa.
"It's football. Brazil lost 7-1 and we lost [on Saturday]. Everybody is going to lose someday," Keshi said.
"We cannot win all the games all the time. This is where we need the media and Nigerians. They have to be behind the team, so that we can go to South Africa and win."
Keshi is expected to make several changes to the line-up that lost to Congo, but refused to be drawn on any specific decisions.
"Who will I start on Wednesday? That information is not for you but for my players," he told supersport.com.
"On Wednesday, you will see who starts but we want Nigerians to know that we are going to South Africa with a positive mindset.
"It's not going to be easy because they also want to win. But we'll see how it goes."
Fenerbahce striker Emmanuel Emenike could be handed a start for the visitors, while defender Godfrey Oboabona is a doubt through injury, with Azubuike Egwuekwe ready to deputise.
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