Banyana Banyana had been forced into the qualification route after their WAFCON quarter-final defeat by Morocco ended their chances of securing a direct place. Nigeria had also entered the play-off contest after suffering a loss to Cameroon the previous Sunday.
Desiree Ellis made one change to her starting line-up, handing Ronnel Donnelly her first start of the tournament in place of Isabella Ludwig.
South Africa dominated possession during the opening period but struggled to turn that control into clear chances, with Nigeria sitting deep.
Asisat Oshoala was also largely contained by the South African defence, and the teams went into the interval without a serious opportunity.
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The deadlock was finally broken four minutes before the hour. Hilda Magaia raced down the left before picking out Thembi Kgatlana, who finished the move to register her third goal of the tournament.
Nigeria almost responded when Kanu headed towards goal in the 74th minute, but Kaylin Swart made an outstanding one-handed stop.
South Africa doubled their advantage with 13 minutes remaining as captain Refiloe Jane pounced on a loose ball and fired home a deflected effort.
Jane was dismissed in stoppage time for handball, allowing Uchiebe to score from the resulting penalty. South Africa will now prepare for the inter-confederation play-offs, which begin in November 2026, with five opponents from other confederations standing between Banyana and World Cup qualification.