The world body ordered the game to be played again because of match-fixing by the referee in the initial qualifier in November 2016.
The win took Senegal to an unassailable 11 points after five games, while South Africa remain rooted at the bottom on four points.
South Africa defeated Senegal 2-1 in Polokwane last November, but Federation Internationale de Football Association ordered a replay because of "match manipulation" by Ghanaian referee Joseph Lamptey, who was banned for life.
Tunisia and Morocco will also reach the World Cup if they avoid defeats against Libya and Ivory Coast respectively on Saturday.
South Africa has lost 2-0 to Senegal, ending their hopes of qualifying for Russian Federation 2018 World Cup.
Meanwhile, Group D's other teams, Burkina Faso and Cape Verde, will do battle in Ouagadougou in another inconsequential match. Sadio Mane of Senegal will be back as he declared himself that he is 100% fit from the injury but Striker Mame Biram Diouf is still out. Despite the seemingly traditionally good results at the upcoming mundiale in Russian Federation, the national team of South Africa we will not see.
Senegal join Egypt and Nigeria in next year's Russian Federation finals.
Bafana Bafana head coach Stuart Baxter says they lacked that one player who could create something out of nothing against Senegal.
He was late in arriving in camp due to appointments with at least two specialists to determine whether he could risk playing in the must-win clash.
Bafana goalkeeper and captain Itumeleng Khune played with a protective white mask after fracturing a facial bone in a club match last weekend.
He laid on a superb, defence-splitting pass for West Ham striker Diafra Sakho to slot past Bafana Bafana goalkeeper Itumeleng Khune, giving Senegal the ideal start after 12 minutes. "I don't think so, maybe I am blue-eyed, but I think with the right sort of application from the players and the co-operation of everybody in South Africa, we can keep moving forward".
Bafana introduced midfielders Andile Jali and Siphiwe Tshabalala midway through the second-half, but neither made an impact.