Guinea-Bissau secured a place at the Africa Cup of Nations for the first time on Sunday after closest rivals Congo Brazzaville lost 2-1 in Kenya.
Congo, needing at least a draw to keep alive their hopes of winning Group E, suffered a surprise defeat despite taking the lead through a controversially awarded penalty.
Guinea-Bissau, who beat Zambia 3-2 on Saturday with a goal from Brito six minutes into stoppage time, have an unassailable four-point lead with one round left.
The team from the tiny former Portuguese colony in West Africa were considered no-hopers by pundits when qualifying kicked off last June.
But solitary-goal home and away victories over Kenya three months ago lifted them to the top of the table while Congo and Zambia drew twice.
Ranked 31st in Africa and 115th in the world, Guinea-Bissau never previously came close to reaching the biennial African football showcase.
Many of the team coached by local Baciro Cande play in Portugal and favour Brazilian-style football names.
The real name of Brito, who is with top-flight outfit Sporting Clube de Braga, is Piqueti Djassi Brito Silva.
Prince Oniangue converted the penalty for Congo only for Ayub Timbe to equalise soon after and Erick Johana scored the second-half Kenyan winner.
Captain Andre ‘Dede’ Ayew opened the scoring as Ghana triumphed 2-0 in Mauritius to also qualify.
The Swansea City midfielder and son of former Ghana superstar Abedi ‘Pele’ Ayew struck from close range after 71 minutes in Belle Vue on the Indian Ocean island.
Two Mauritians failed to cut off a cross and Ayew controlled the ball before firing a left-foot shot past outstanding goalkeeper Kevin Jean-Louis.
Dominant Ghana sealed victory three minutes later through Chelsea midfielder Christian Atsu, who was voted the outstanding footballer of the 2015 Cup of Nations.
Mauritius were battling to contain Ghanaian raids on the left flank and from one the ball was cut back for Atsu to score with a hard, low shot.
Although they never threatened to breach the Black Stars defence, Mauritius were a much improved team from that humiliated 7-1 in Ghana last June.
Ghana have 13 points in Group H, Rwanda and Mauritius six each and Mozambique four with one matchday to come in September.
Zimbabwe were another country to book a place in the finals after whipping Malawi 3-0 in Harare while Group L rivals Guinea fell 1-0 in Swaziland.
Knowledge Musona was fouled inside the box and converted the penalty on 16 minutes to set up the convincing home victory.
Recently crowned South African Footballer of the Year Khama Billiat doubled the lead on 36 minutes, firing a cut-back into the net from close range.
Roared on by a 40,000 crowd at the national stadium, Zimbabwe struck again a minute from time through a Cuthbert Malajila header.
Morocco, Algeria, Cameroon, Egypt and Senegal have also qualified for the January 21-February 12 tournament while Gabon are automatic participants as hosts.