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 have 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.
Nigeria travelled by sea to west African neighbours 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.