Both were involved in the move that led to a Thamsanqa Mkhize own-goal before half-time.
Victory sent Senegal five points clear of Burkina Faso and Cape Verde in Group D with one round left.
Senegal’s only appearance at the finals came in 2002 when coach Aliou Cissé captained a team to the quarter-finals in South Korea and Japan.
South Africa defeated Senegal 2-1 in Polokwane last November, but world football’s governing body Fifa ordered a replay because of match manipulation by Ghanaian referee Joseph Lamptey, who was banned for life.
"It was not an easy game for us, but we took the chances that came our way," said Mane, who returned to Premier League action last Saturday after a hamstring injury.
"Our coach stressed before the match the importance of qualifying for the World Cup and we gave everything throughout the match."
Senegal are the third African qualifiers for the World Cup in Russia after Nigeria and Egypt, who booked their places last month.
The other two spaces will be filled on Saturday. Tunisia and Morocco are in the driving seats in their respective groups.
Pacesetters Tunisia, who host Libya in Group A, hold a three point advantage over the Democratic Republic of Congo, who play Guinea in Kinshasa.
Morocco are one point in front of Cote D’Ivoire in Group C. A stalemate in Abidjan will send the north Africans to the World Cup for the first time since 1998. The Ivorians will be seeking a fourth consecutive appearance at the football fest.