The South Africans go through to the fourth and final round. Banyana meet the Super Falcons in Nigeria first and then in South Africa on dates to be confirmed between April 1 and April 9, with the winners of the tie progressing to the Paris Olympics.
Banyana, the reigning African champions, had a bye through the first round and beat Democratic Republic of Congo 3-1 on aggregate in the second round.
The summer Olympics are being held from July 26 to August 11.