Victor Osimhen scored the first penalty of the game with just 15 minutes on the watch to put Nigeria 1-0 ahead.
After the substitution of Kelechi Iheanacho in the 87th minute, Ahmed Musa scored the second penalty in the 94th minute to put the game to bed.
Victory in the game means 12 points for Nigeria but Cape Verde's win against the Central African Republic translates that the Super Eagles will have to wait till the last game to seal qualification.
Super Eagles will have their final group phase encounter against Cape Verde’s Blue Sharks in Lagos on Tuesday.
With only the group winners proceeding to the knockout phase, Cape Verde will have to defeat Nigeria on Tuesday with the Eagles needing just a draw to secure their qualification.