Federation Internationale de Football Association ordered the qualifier to be played again because of match-fixing by the referee in the initial match in November 2016.
South Africa knew it had to win its last two games to have any chance of making it to Russian Federation, but defeat in Polokwane ends its slim hopes of qualification.
After a cagey opening 10 minutes from both teams, the Teranga Lions took the lead with their first attack on goal after Sadio Mane's defence-splitting pass left West Ham forward Diafra Sakho with the relatively simple task of side-footing past Itumeleng Khune in the 12th minute.
"I don't want to say that we can't win the match but it is not going to be easy". Coach Aliou Cisse knelt and held his arms up.
But Senegal proved too strong, and Mane celebrated an historic victory, with his country's last time at a World Cup finals coming in 2002.More news: Flipkart to launch its own smartphone under the Billion brand
Morocco are one point in front of the Ivory Coast ahead of a showdown in Abidjan with the visitors hoping to end a 20-year absence from the World Cup.
Senegal is the third African nation to secure qualification to the world's most prestigious competition after Nigeria and Egypt who managed to accomplish the target.
What if they'd won the two qualifiers against Cape Verde two months ago? Either Tunisia or Congo and Morocco or Ivory Coast will make up Africa's contingent in Russian Federation.
Lebogang Manyama, Percy Tau, Themba Zwane and Sibusiso Vilakazi failed to put the finishing touches to their lovely interplays. But one of the teams that they've qualified at the expense of - South Africa - couldn't have had worse luck.
South Africa introduced midfielders Andile Jali and Siphiwe Tshabalala midway through the second half, but neither made an impact. But the decision to replay a game because of fixing caused serious discontent among the three other teams competing against Senegal for a World Cup place. CAS has not announced any decision regarding Burkina Faso's appeal and it's unclear what would happen if sport's highest court upholds the appeal.