The world footballing mother body made the ruling last week, which was based on the fact that the referee who officiated South Africa's 2-1 win over Senegal in November a year ago, Joseph Lamptey, has been handed a lifetime ban for match manipulation.
Senegal and South Africa are now third and fourth respectively in Africa's Group D behind Burkina Faso and Cape Verde Islands.
The world football governing body, FIFA, ordered the replay after it banned the referee for the original game, Joseph Lamptey, for manipulating the match.
Neither South Africa nor Senegal have been accused of any wrongdoing. He determined that Napoli and Senegal defender Koulibaly had handled the ball in the area, when it clearly had not happened.
They said the decision was taken on moral and ethical grounds of not wanting to benefit from match manipulation, even though Federation Internationale de Football Association had not established any wrongdoing on the part of South Africa.