Amajita pulled off a great performance at Bidvest Stadium to beat Congo 1-0, courtesy of a goal from Platinum Stars striker Thabani Mthembu.
South Africa needed to score at least one goal, as well as not concede any, to advance to the next stage of the Youth Championship qualifiers.
Amajita lost 2-1 in the first leg away in Congo a fortnight ago.
South Africa will now wait to see who the winner is between Tanzania and Nigeria to find out their next opponent in the qualifiers.
The Nigerians currently hold a 2-1 lead over Tanzania, after they won the first leg in Dar as Salaam.
The two teams meet again for the second leg in Lagos today.
Luvhengo praised his team for a gallant performance in Johannesburg yesterday.
"We knew that they would come to defend and try to catch us on counter-attack," the coach says. "We had to play our passing game and try to stretch them on the wings.
"After we scored the goal, they opened up at the back and I believe we could have scored at least three more goals."
Luvhengo says he is confident his charges can go all the way in the tournament, and the Under-20 World Cup after that.
"I must congratulate the boys for the victory and, with the same attitude and commitment, I believe we can go far in the tournament.
"We just need to win two games to qualify for both the African Youth Championship Finals and pave our way to the World Cup tournament."