With the Falconets aiming to make their ninth Fifa U20 Women's World Cup appearance, Rasheedat Ajibade and Anam Imo were the heroines at the Old Peter Mokaba Stadium.
Despite the win, the gaffer, who lauded his players for playing to instructions, insists they still have a lot of work to do in the bid to guarantee their World Cup qualification.
"It was a good match for both teams (South Africa and Nigeria) and a wonderful result for us," Danjuma told Goal.
"I dedicate the victory to the girls for holding their own and playing according to plan. It was not easy playing against a technically sound opponent like South Africa.
"We were not surprised about their tactics because we watched some of their clips before the match like their loss to Burundi in Bujumbura and friendly against Ghana.
"We know they have some quality players and worked hard to make sure we allow them no space to give us much problem. Our approach really worked for us. Despite we won, I must acknowledge that South Africa played well, especially in the second half.
"However, I am proud of the girls because they stick to plan and played to instructions all through the match. Though I'm glad we didn't concede in the match we still have few areas to correct before the second leg.
"I still believe we have not achieved anything because nothing is uhuru yet until we win the second leg in Benin City and ensure we qualify for the World Cup in France," he concluded.