The West African side failed to win a single one of their opening three Group A matches, casting doubt over whether they would get the chance to defend the title they won in South Africa in 2013.
Nigeria now sit second following victories over Sudan and Congo, but know anything less than a win against the already qualified South Africa on Wednesday could end their hopes of making the tournament in Equatorial Guinea.
Congo - third by virtue of their inferior head-to-head record against Nigeria - head to Sudan knowing they must better Nigeria's result.
Group E remains wide open, with all four teams still harbouring dreams of qualification.
Ghana lead the way with eight points and a draw against Togo - bottom on six - would be enough to see them through, although they come into the fixture on the back of a 1-0 defeat in Uganda, and defeat would ensure they finish outside the top two.
It is impossible for Guinea and Uganda to qualify together automatically, so their encounter on Wednesday is effectively a play-off.
Those who miss out in Groups A and E could be afforded a reprieve, as the pools lead the way in the chase for the best third-placed nation.
Algeria have run away with Group B and head to a Mali side desperate to edge Malawi to qualification.
Second-placed Mali hold a four-goal advantage over their rivals, who visit Ethiopia, so a win should be enough to see them progress.
Group D leaders Cameroon have already booked their place at next year's tournament and host Ivory Coast in Abidjan this week.
The Ivorians sit three points clear of third-placed Democratic Republic of Congo, but a defeat coupled with a win for their nearest rivals over Sierra Leone would see them miss out on a top-two finish, owing to their having scored fewer goals in matches between the two nations.
Cape Verde and Zambia meet in Group F having already made certain of their finals place, while Mozambique aim to enhance their slim chances of finishing as the best third-placed team at Niger.
It is a similar story in groups C and G, with Burkina Faso, Gabon, Tunisia and Senegal having already qualified, and Angola and Egypt scrapping in third.
Angola head to Burkina Faso in Group C, while Lesotho are at Gabon, and Group G sees Tunisia host Egypt and Senegal face Botswana.