West Ham striker Sakho opened the scoring off a pass from Liverpool attacker Mane and both were involved in the move that led to a Thamsanqa Mkhize own-goal before half-time yesterday.
Victory gave Senegal an uncatchable five-point lead over Burkina Faso and Cape Verde in Group D with one round left.
The only previous World Cup appearance by Senegal was in 2002 when current coach Aliou Cisse captained a team that reached the quarter-finals in South Korea and Japan.
Bottom-of-the-table South Africa lie seven ponts behind Senegal ahead of a return match in Dakar next Tuesday, with Burkina Faso hosting Cape Verde at the same time.
"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.
"We are going to represent all of Africa in Russia next year and will do our best to make everyone proud."
Senegal are the third African qualifiers for the World Cup in Russia after Nigeria and Egypt, who secured places during the penultimate qualifying round last month.
The other two slots will be filled Saturday with north African countries Tunisia and Morocco needing draws to qualify.
Tunisia host out-of-contention Libya in Group A holding a three-point advantage over the Democratic Republic of Congo, who play Guinea in Kinshasa.
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 took the lead after 12 minutes when Sakho raced on to a Mane pass and side-footed the ball to the right of onrushing Khune.
Goalkeeper Khadim Ndiaye failed to grasp a fierce close- range Themba Zwane shot, but recovered to catch the rebound after the ball struck the onrushing Percy Tau.
The Senegalese Teranga Lions doubled their lead after 38 minutes against the run of play with another goal involving Sakho and Mane.
Sakho broke clear and crossed to Mane, whose shot was blocked by Khune only for the clearance to hit Mkhize and trickled back into the net.
As half-time approached, Manyama went close again to scoring, this time from a free-kick that Ndiaye tipped over.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)