They have now recorded six points from two matches, while Cameroon are second on two points after they forced Zambia to a 1-1 draw at home.
Zambia are third on a point ahead of Algeria, who also have a point.
The qualifying tournament will resume in August 2017 with Nigeria hosting Cameroon and Zambia at home to Algeria.
After a rather shaky start, the home team took the game to their opponents and they were rewarded after 25 minutes, when the lively Victor Moses was released by his fellow Chelsea star Mikel Obi to fire past Algeria goalkeeper M’Bolhi.
He certainly made up for his big miss in the seventh minute.
The Super Eagles doubled their lead three minutes from the interval when Mikel controlled the ball on top of the box and after a moment of hesitation rolled the ball beyond the Algerian shot stopper.
However, Algeria pulled a goal back in the 67th minute, when Nabil Bentaleb smashed home an unstoppable scorcher from distance.
Man of the match Victor Moses will then put the game beyond the North Africans in stoppage time, when he fired home off a low cross by substitute Ahmed Musa.
The outcome of this game would probably have been a lot different had the visitors made the most of two clear-cut chances in the first half.
First, Nabil Bentaleb threw away a sitter from inside the Nigeria box when the easier thing was for him to score after 36 minutes.
And minutes later, Riyad Mahrez came close to getting on the score sheet, but his shot from inside the box missed the target narrowly with the Nigeria defence at his mercy.
When Algeria pulled a goal back they pegged their hosts in their own half of the pitch with the dangerous Yacine Brahimi tormenting the Eagles defence and Riyad Mahrez in full charge of the midfield.
Goalkeeper Akpeyi, deputising for injured Carl Ikeme, tipped for a corner a free kick with nine minutes left on the clock and in the closing moments of this encounter Nigeria took the game again to their opponents before they were rewarded with a back-breaking goal by the impressive Victor Moses.
Eagles vs Algeria (4-2-3-1)
Daniel Akpeyi – Kenneth Omeruo (Shehu Abdullahi 66), Elderson Echiejile, Leon Balogun, William Troost-Ekong – Ogenyi Onazi, Mikel Obi (Wilfred Ndidi 83) – Oghenekaro Etebo, Victor Moses, Alex Iwobi (Ahmed Musa 75) – Kelechi Iheanacho