The sloppy Super Eagles were punished in front of their home crowd in Lagos when Karl Namnganda scored the winner in the 91st minute of the game.
Despite the defeat Nigeria are still on top of the Group C with six points after three games followed by Cape Verde and Central African Republic, who have each four points, while Liberia are bottom with three points.
They are now set to play a crucial reverse leg on Sunday at Central African Republic.
In Group J, Benin have claimed a precious away victory against Tanzania 1-0 courtesy to a goal from Brest forward Steve Mounie in the 72nd to extend their lead at the top.
Benin have collected 7 points from their first three games to move two points clear above DR Congo who claimed their first victory of this group stage against Madagascar 2-0.
They will host Tanzania on Sunday to boost their chances in advancing to the third and final phase of the World Cup qualifiers.
Only the winners of the 10 groups advance for the play-off phase where they meet each other and the five winners qualify for the 2022 World Cup in Qatar.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.
Short link: