Coach Desiree Ellis gave Ronnel Donnelly her first start of the tournament in place of Isabella Ludwig and was the only change from the team that lost to Morocco in the quarterfinals.
Nigeria were happy to sit back, stay compact and see what Banyana had to offer in the first half and neither side were able to create any meaningful chances as the halftime whistle blew.
It took until just before the hour mark when the game sprang to life. Hilda Magaia broke free down the left and teed up Thembi Kgatlana who scored her third goal of the tournament.
Nigeria pushed for an equaliser and nearly got it on 74 minutes when Kanu rose highest but goalkeeper Kaylin Swart pulled off a superb one-handed save.
Banyana increased their lead in the 77th minute when captain Refiloe Jane pounced on a loose ball and unleashed a powerful strike that took a deflection and sailed into the back of the net.
Jane's joy turned to sorrow in stoppage time when she was sent off for handling the ball and giving away a penalty, which Christy Ucheibe buried.
South Africa saw out the remaining minutes and can now look forward to the inter-confederation play-offs, which get underway in November.
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