Cameroon were the last of the quintet to qualify for the last eight, sneaking through on Thursday by the margin of one goal only after a close-run finish in Group D.
Four of the five - Algeria, Cameroon, Ghana and Nigeria - lost their opening game at the tournament and were forced to come from behind to finish among the top two in their respective groups.
Ivory Coast are the only one of the teams heading to the World Cup finals in South Africa later this year who have so far not been beaten at the tournament.
But they have played just two matches in Angola because of the withdrawal of Togo before the tournament started, being held to a goalless draw by Burkina Faso before beating Ghana.
Algeria qualified for the last eight on the back of just a single goal, scored by defender Rafik Halliche when they beat Mali in their second Group A match.
The north Africans started with a shock 3-0 loss to Malawi and qualified on the back of an unconvincing goalless draw with hosts Angola.
But Algeria, who will have England and the United States among their group opponents at the World Cup in June, insist they have overcome their stuttering start.
"The conditions have been difficult but we've kept working. We've been improving match-by-match," coach Rabah Saadane said after their qualification for the last eight.
Cameroon only made it by virtue of having scored one more goal than Gabon in a count-back after a three-way tie at the head of their group.
"The players must be commended for doing what was necessary to qualify," said coach Paul LeGuen after Cameroon twice came from behind on Thursday to draw 2-2 with Tunisia.
Ghana had to wait almost a week before they started their campaign, losing 3-1 to the Ivorians in Cabinda.
They then lost captain Michael Essien with a knee injury before sneaking through 1-0 over Burkina Faso in their last Group B game.
Nigeria were thoroughly outplayed by Egypt in their opening game but still finished second after next beating Benin and Mozambique.
Egypt, who are seeking an unprecedented third successive Nations Cup title, have overshadowed the World Cup-bound teams and will start the quarter-finals as favourites to retain their title.
Hosts Angola take on Ghana in the first quarter-final in Luanda on Sunday, followed by the meeting in Cabinda between the Ivorians and Algeria.
On Monday, Egypt take on Cameroon in Benguela and Zambia play Nigeria in Lubango.
The semi-finals will be played next Thursday with the final in Luanda on January 31.
