Nigeria now have six points from two matches, while Liberia are second with three points.
Central African Republic are third on a point, same as bottom team Cape Verde.
The home team stunned the Super Eagles in the 20th minute, when Dylan Tavares raced past the defence before he shot beyond goalkeeper Maduka Okoye by the near post.
Below is the group’s current standings, after two matches each by the four teams:
Team P W D L GF GA GD Pts
Nigeria 2 2 0 0 4 1 +3 6
Liberia 2 1 0 1 1 2 -1 3
Cape Verde 2 0 1 1 2 3 -1 1
Central African Republic (CAR) 2 0 1 1 1 2 -1 1