England-based striker Yakubu wrapped up Nigeria's win
Nigeria clinched the top spot of Group Three of the Nations Cup qualifiers on Tuesday after Uganda could only manage a goalless draw away to Lesotho.
The match, which was originally scheduled for Sunday, had to be postponed after the Tanzanian match officials arrived late for the game in Maseru.
The result leaves second-placed Uganda with eight points, four adrift of leaders Nigeria.
The Super Eagles thus finish as group winners with one match remaining.
The Cranes can still claim one of two remaining best second-placed berths that would see them qualify for the finals in Ghana.
Sudan or Tunisia, who are on 12 and 13 points respectively in Group Four, are certain to claim one of the best runners¿ up berths.
Uganda must beat Niger at home in their final qualifier in September.
But the Cranes will have to improve on their performance if they are to defeat the Menas after a scrappy performance in Maseru.
Geoffrey Massa fluffed the best chance for the visitors on the hour mark as his attempted volley went wide after being left unmarked in the Lesotho box.
On Sunday, Nigeria beat Niger 3-1 to keep their lead in the group - but they were made to work for it by their neighbours.
Niger held Nigeria's famous attack - which included England-based strikers Kanu, Obafemi Martins and Yakubu Aiyegbeni - at bay until just before half time, when Kanu headed in Onyekachi Okonkwo's cross.
But the Menas came out fighting after the break, and midway through the second half got their reward when Kamilou Daouda headed in.
Parity was restored for barely more than a minute, however, before Nigeria went back in front through a penalty.
Osaze's corner kick caused all sorts of confusion in the Niger defence, and the referee spotted a handball during the resulting melee.
Taiye Taiwo stepped up and converted.
But Niger still kept pressing, and Nigeria were not allowed to relax until Yakubu Aiyegbeni beat the Nigerien defence to slot past a helpless Rabo in the Niger goal.