Central defender Janine van Wyk scored the all-important goal in the 23rd minute, after Nigeria failed to clear their lines from a South African corner, and Van Wyk was on hand to strike the ball from 25 metres out with her left foot, and watch as it dipped in off the underside of the crossbar past goalkeeper and captain Precious Dede.
The Sasol-sponsored Banyana Banyana will face Equatorial Guinea in the Final in Malabo on Sunday, November 11, after the hosts defeated Cameroon 2-0 in the first semi-final played earlier in the day.
The victory marked Banyana's first triumph over Nigeria, the number-one ranked side in Africa, since their international debut in 1993.
Particularly in the second half, the Nigerians came to the fore with attacking play but found Banjyana keeper Thoko Mndaweni in fine form between the posts.
The Nigerian attacks were often neutralised by some fine defensive work, with centre-back Amanda Sister combining superbly with Van Wyk, aided well by fullbacks Gabisile Hlumbane Van Wyk's clubmate Nothando Vilakazi.
With the speed of striker Jermaine Seoposenwe a major problem for the Nigerian rearguard, and with the experienced Portia Modise dominating the midfield tussles along with captain Amanda Dlamini and young tough-tackling Refiloe Jane, the South Africans saved their best performance at the tournament for the clash with the Nigerians.
Van Wyk is becoming a thorn in Nigeria's flesh from a goal-scoring perspective, having netted with a superb free-kick against the Super Falcons at the 2012 CAF African Women Championship held in Ekurhuleni.
"I have been in the Banyana Banyana side since 2004 and we have tried for so long to beat the Nigerians but luck has never been on our side, but now we have proved that we can compete and beat of the best on the continent," said Van Wyk, whose strike was her ninth in a Banyana Banyana jersey.
Speaking after the game, Banyana coach Joseph Mkhonza said: "Seeing Banyana beat Nigeria for the first time in our team's history has left us with an amazing sense of pride and confidence ahead of Sunday's Final against the hosts Equatorial Guinea. All of our players need to be commended for their commitment and discipline shown.
"We had to pick ourselves up after the opening match defeat against Equatorial Guinea and have applied ourselves to beat Senegal, the Democratic Republic of Congo and now Nigeria.
"We have some homework to do before Sunday's Final, knowing we will play in front of a large red-clad crowd in what is certain to be a packed Malabo Stadium, but we will be ready for the challenge," added Mkhonza.