The 'Cranes' went all the way to the 1978 final before failing against hosts Ghana and they can end 33 years in the wilderness by dodging defeat away to Angola Sunday.
Coached by Scot Bobby Williamson, Uganda have gathered 10 points from four Group J games and Angola (six), Kenya (four) and Guinea Bissau (three) trail.
Goals from David Obua, Andrew Mwesigwa and Geoffrey Ssernunkuma last September enabled Uganda to whip Angola 3-0 during the opening qualifiers for the 2012 tournament.
Angola were outclassed on a wet Kampala afternoon and Williamson senses it will be much tougher for his team in Luanda.
"We still have a short distance to travel and the hard bit will be crossing the line," warned the 49-year-old former Kilmarnock and Hibernian coach.
"Angola is going to be a tough game because not many national teams win away in Africa. A point will see us through but I hope we can put our opponents on the back foot.
"I believe my players are sufficiently experienced and have had enough disappointments in the past not to falter again."
Even a defeat would not spell the end for Uganda—just leave them needing a home win over great regional rivals Kenya during October to secure first place.
Uganda are skippered by Austria-based defender Ibrahim Sekagya and rely on team work rather than individuals with the squad having no big-name footballers.
Senegal are the other country going into a 21-fixture, penultimate-round qualifying schedule knowing they can qualify without assistance.
But they must defeat second-placed Democratic Republic of Congo in Dakar to create an unassailable lead in Group E where four-time champions Cameroon are only third.
However, Senegal's hopes of getting the win they require were boosted by turmoil in their opponent's camp on Wednesday.
Widely-travelled French veteran Robert Nouzaret quit as coach - to be replaced by another veteran of African football Claude Le Roy - after football officials there ordered him to choose only local-based footballers.
While Senegal must do without suspended striker Mamadou Niang, DR Congo welcome back talismanic midfielder Mputu Mabi after a 12-month ban for assaulting a referee.
Cape Verde Islands, Guinea, Zambia and South Africa can also seal places at the 16-team biennial African showcase if they triumph and the other group result assists them.
The Cape Verdians must win in Mali and hope Zimbabwe and Liberia draw while Guinea have to beat Ethiopia at home and hope Nigeria do not collect maximum points in Madagascar.
A Zambian win on the Comoros Islands seems feasible, but they need Libya to lose a home game against Mozambique moved to Cairo because of the anti-Moamer Kadhafi uprising.
A South African side lacking injured captain Steven Pienaar must collect three points in sauna-like Niger and rely on experimental Egypt to prevent Sierra Leone winning at home.
Needing three points to have any hope of qualifying and seeking a fourth consecutive title, Egypt appear resigned to their fate and chose Olympic and youth stars.
Burkina Faso are the other possible qualifiers and wwould do so without kicking a ball as they cannot be caught in Group F if Gambia fail to win in Namibia.
Morocco and Tunisia lead other sections on goal difference ahead of away games against closest challengers Central African Republic and Malawi respectively.
Ghana, runners-up to Egypt last year, get the ball rolling with a Friday fixture against Swaziland in Group I where co-leaders Sudan have a tougher task away to Congo Brazzaville.
Didier Drogba-led Ivory Coast and surprise side Botswana have secured places at the January 21-February 12 Cup of Nations with co-hosts Equatorial Guinea and Gabon.