Janine van Wyk scored the only goal of the match with a long-range strike in the 23rd minute to hand the SA women their first ever win over defending champions Nigeria, the top-ranked team in Africa.
"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," said Van Wyk, who also scored against Nigeria at the 2010 African Championships.
"Now we have proved that we can compete and beat the best on the continent."
Banyana will face Equatorial Guinea, who beat Cameroon 2-0 earlier in the day, in the tournament final in Malabo on Sunday.
"All of our players need to be commended for their commitment and discipline shown," said head coach Joseph Mkhonza.
"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."