Woman of the Match Asisat Oshoala struck a brace for the dominant Super Falcons, with Refiloe Jane pulling one back after the break for Banyana.
The top three finishers at the competition will qualify for the 2015 Women's World Cup in Canada.
Oshoala opened the scoring in the 38th minute, as her shot in the box deflected off Banyana captain Janine van Wyk and past the helpless Thokozile Mndaweni, who made a number of fine saves beforehand.
Oshoala doubled the advantage with an ambitious chip on the stroke of half-time.
Banyana threatened on occasion, as Portia Modise thundered a strike narrowly wide midway through the first stanza, while Van Wyk drew an unconvincing save from Ibubeleye Whyte with a dipping effort shortly before the recess.
Banyana reduced the deficit in the 68th minute, as Jane's shot on the angle was controversially adjudged to have crossed the line.
Vera Pauw's charges, however, were unable to draw level come the end of 90 minutes.
Nigeria: Ibubeleye Whyte, Ugo Njoku, Ebere Ngozi, Onome Ebi, Josephine Chukwunonye, Evelyn Nwabuoku, Halimatu Ayinde, Ngozi Okobi, Francisca Ordega, Asisat Oshoala, Desire Oparanozie.
South Africa: Thokozile Mndaweni , Simphiwe Dludlu, Nothando Vilakazi, Janine Van Wyk, Noko Matlou, Amanda Dlamini, Mpumi Nyandeni, Refiloe Jane, Leandra Smeda, Portia Modise, Shiwe Nogwanya.