Gabon, who are co-hosting with Equatorial Guinea, must first get past Morocco, who were expected to dominate the group but suffered a surprise reversal in their first game on Monday.
Morocco will be eliminated if they lose again and become, after Senegal, the second heavyweight casualty of the tournament.
"It is like a final for us," said Morocco coach Eric Gerets on the eve of the match against a Gabon team expecting 40,000 fans behind them in the capital's new stadium.
Tunisia, who won the Nations Cup when they hosted it eight years ago, have a more modest task when they face Niger, who by their own admission were out of their depth on Monday in losing their debut match at the finals.
A Tunisia win combined with success for Gabon will take the two teams through but any other result leaves the permutations still open.
Ivory Coast went through to the last eight on Thursday by beating Burkina Faso 2-0 while Angola are well placed to join them from Group B after a 2-2 draw with Sudan.
Both matches were played in Malabo.
Co-hosts Equatorial Guinea were the first side to book their place in the knockout round by beating Senegal on Wednesday.
