Albania-based Reginaldo Faife kept Mozambican hopes alive of a top-two finish and a place at the finals in Cameroon by scoring the only goal after 63 minutes in Maputo.
Guinea-Bissau and Namibia have eight points each after a 0-0 draw in Windhoek on Saturday, Mozambique seven and Zambia four with one matchday to come next March.
Defeat was a huge blow for Belgian-born Zambia coach Sven Vandenbroeck, who was hired when local Wedson Nyirenda resigned after the opening round to join a South African club.
Vandenbroeck has won one match, drawn one and lost two in the Cup of Nations since his first appointment as a national team head coach.
He assisted compatriot and Cameroon coach Hugo Broos when the central African country surprisingly won the 2017 Cup of Nations in Gabon.
Zambia were shock winners of the 2012 Cup of Nations in Libreville, edging the Ivory Coast on penalties after a goalless final.
In another early match, Ghana defeated Ethiopia 2-0 in Group F in Addis Ababa with recalled Jordan Ayew scoring twice during the first half.
Sudan ended a four-match losing run in Group A with a surprise 3-1 away victory over already-qualified Madagascar in Antananarivo.
A stoppage-time goal salvaged a 2-2 Group H draw for the Central African Republic in Rwanda while Niger came from behind to win 2-1 away to Swaziland in Group J.
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