They will join neighbours Morocco, who qualified last Friday without kicking a ball, in the field of 24-team for the finals in the Ivory Coast next January.
Algeria's Baghdad Bounedjah slipped through the defence in the fifth minute to put the visitors ahead as they costed to victory in Tunis, where Niger hosted the game after their own stadium was deemed inadequate for international competition.
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Algeria had to come from behind to beat the same side at home last week -- with Riyad Mahrez scoring an 88th-minute winner -- and as a result coach Djamel Belmadi made eight changes for Monday's Group F match, emphasising the depth at his disposal.
Nigeria, also brimming with European-based players, were humbled last Friday in a shock home defeat by Guinea Bissau but reclaimed top spot in Group A with a 1-0 win in the return leg. Moses Simon's 30th minute penalty moved them to nine points.
Ghana top Group E after coming from behind to draw in Angola, who were ahead through a 51st penalty from Reading's Lucas Joao in only the second appearance for the former Portugal international who has switched allegiance.
Osman Bukari equalised some 20 minutes later and Ghana, in their second game under new coach Chris Houghton, hit the woodwork late on as they looked to snatch victory in Luanda.
They top Group E on eight points with the Central African Republic moving into second spot after beating Madagascar 2-0 in neutral Cameroon with a double from Louis Mafouta. They have seven points with Angola down in third place on five.
Tuesday will see a further 13 matches to complete the fourth of six rounds of qualifying.