Malian Moussa Kone and Namibian Elmo Kambindu scored twice each as their countries built first-leg leads with away wins this weekend in 2020 African Nations Championship qualifying.
While Mali, Namibia, Uganda and Ethiopia returned home with aggregate advantages and Mauritania and Zambia forced away draws, Burundi were the only home side to succeed.
Kone put 2016 runners-up Mali ahead within two minutes in Guinea-Bissau and added a second before half-time.
Issiaka Samake and Dusse Kodjo netted inside six minutes midway through the second half to complete a 4-0 victory that virtually assures Mali of a place in the final qualifying round.
Mauritania are the likely opponents of Mali during September and October after forcing a 0-0 draw away to debutants Cape Verde in Praia.
Kambindu netted twice during the second half as Namibia avenged an away defeat by the Comoros in 2018 qualifying with a 2-0 victory in Moroni.
It was an impressive showing by the visitors, who went ahead on the hour and sealed success with a second goal 10 minutes from time.
Assuming Namibia do not slip up at home next weekend, they will face Madagascar or Mozambique for a place at the 2020 tournament in Cameroon.
Goals from Patrick Kaddu, Mustafa Kizza and Taddeo Lwanga earned Uganda a 3-1 win over Somalia, who staged their home match in neighbouring Djibouti for security reasons.
– Stubborn home side –
Kaddu and Lwanga were part of the Uganda squad that reached the last 16 at the Africa Cup of Nations in Egypt this month before losing narrowly to eventual runners-up Senegal.
While there are no Cup of Nations selection restrictions, the Nations Championship is confined to footballers playing in their country of birth.
Ethiopia, the original 2020 hosts who were replaced by Cameroon after falling behind with preparations for the biennial 16-team tournament, edged Djibouti 1-0 in Djibouti City.
It took the Ethiopians 76 minutes to break down a stubborn home side with Aschalew Tamene snatching the match-winner.
Botswana were held 0-0 by Zambia in Francistown in a repeat of the COSAFA Cup regional tournament final in South Africa last month.
Zambia won the final 1-0 and will be expected to take advantage of playing at home next weekend to book a showdown with eSwatini (formerly Swaziland) or Angola.
Burundi were the only side to maximise home advantage, overcoming South Sudan 2-0 in Bujumbura through second-half goals from Olivier Dusabe and Jospin Nshimirimana.
A further eight first legs are scheduled for Sunday, including a clash of arch east African rivals Tanzania and Kenya in Dar es Salaam.
The Central African Republic received a walkover when Sao Tome e Principe said financial constraints prevented them travelling to Bangui for the first leg.