First-half strikes from Rasheedat Ajibade and Anam Imo gave the Falconets a huge first-leg advantage ahead of their reserve fixture in Benin City in a fortnight.
The visitors came close to securing the lead in the 20th minute but the attack of the Falconets was stopped by Basetsana defender Antonie Maponya.
Six minutes later, Ajibade forced hosts' goalkeeper Mapaseka Mpuru to a save before the FC Robo star eventually put Nigeria in front on the half-hour mark.
In the 35th minute, Imo doubled the Falconets lead having benefited from a defensive blunder by the hosts.
Linda Malthalo almost brought them back into the contest with a free kick that went inches wide three minutes later.
After the interval, Karabo Dlamini had a good chance from another spot-kick but saw her attempt sail wide.
Despite coach Muade Khumalo's introduction of Gabriela Salgado and Thambolinye Mzoneli, the west African giants remained solid and ran away with the victory.
With the win, Christopher Danjuma's side are one step ahead of their South Africa counterparts for a spot in France.
Both sides will clash in the second leg at the Samuel Ogbemudia Stadium on January 27. The winner on aggregate will book one of the two tickets as African representatives for the finals scheduled to hold from August 5-24.