The Super Eagles, who needed a win to reach the quarter-finals, scored first through Chisom Chikatara's fourth goal of the tournament in the 51st minute.
Tunisia had a goal disallowed in the 44th minute when leading marksman Ahmed Akaichi was ruled offside.
Niger and Guinea fought out a 2-2 draw in an entertaining encounter which further complicated the calculations.
It was the second drawn game for Guinea who held more control in the opening stages but fell behind when Youssef Alio gave Niger the lead after 36 minutes.
Guinea struck back a minute later through Aboubacar Sylla.
Niger restored their lead in the 49th minute through Adamou Musa but Aboubakar Bangoura levelled with a 75th-minute strike.
Nigeria have four points and need to beat second-placed Guinea on Tuesday to qualify to the quarter-finals as group winners.
Third-placed Tunisia will play bottom-of-the-table Niger in the second match.