The Super Eagles, who went into the finals in Cameroon as one of the favourites to win the tournament, were undone as Youssef Msakni's long range effort slipped through the fingers of Maduka Okoye.
There was also an early exit for Everton midfielder Alex Iwobi, who was sent off just SEVEN minutes after being substituted onto the pitch.
The former Arsenal man was initially given a yellow card after his challenge left Ellyes Skhiri in a heap.
However, referee Maguette Ndiaye was instructed to look at the tackle on the VAR pitchside monitor. Ndaye then brandished the red instead as Iwobi and Nigeria's AFCON journey came to a sudden end.
Tunisia will face Burkina Faso, who beat Gabon 7-6 on penalties, in the last eight on January 29.
Nigeria looked strong in the early stages of the tournament as they won all three of their group matches, including a win against Mohamed Salah's Egypt.
However, their AFCON journey is now over, their defeat made all the more embarrassing by Tunisia being affected by a COVID outbreak in the squad.
Clear-cut chances were few and far between with Nigeria forward Umar Sadiq firing across goal and wide in stoppage-time, while Moses Simon had an earlier effort blocked by Bechir Ben Said.
But Tunisia made it count when it mattered as Msakni's speculative 25-yard effort went through a crowd and into the net as Okoye failed to get a strong enough hand on the shot.