The result in Maseru guaranteed the Super Eagles a top-two finish in the section ahead of their top-of-the-table clash away to Benin in Porto-Novo later Saturday.
Nigeria has eight points, Benin seven, Sierra Leone four and Lesotho three. The countries finishing first and second qualify for the 24-team tournament in Cameroon next January.
Benin needs one point from the match against Nigeria to also secure a place at the finals of the premier African national team competition.
The Super Eagles travelled by sea to Benin on Friday after players raised concerns about the poor road network linking the countries.
Algeria, Burkina Faso, Cameroon, Comoros, Egypt, Equatorial Guinea, Gabon, Gambia, Ghana, Guinea, Ivory Coast, Mali, Morocco, Nigeria, Senegal, Tunisia, and Zimbabwe have qualified, leaving seven places to be filled.