Four-time African champions Ghana went into their away game against already-qualified Angola looking for a first win of the 2025 preliminaries.
Their tenuous hopes were lifted after 19 minutes when Leicester City's Jordan Ayew scored with a stunning freekick, but a close-in header from substitute Zini in the second half secured Angola a 1-1 draw that ended Ghana's run of 10 successive Cup of Nations finals appearances.
Nineteen teams have now secured their place for next year's tournament that will take place in Morocco.
Mali won 1-0 away in Mozambique despite fears for their safety amid on-going unrest in Maputo following disputed election results.
Kamory Doumbia scored the only goal of a game that Mali wanted postponed, or at least played behind closed doors, for fears the rioting might spread to the crowd.
Mali coach Tom Saintfiet told Reuters earlier on Friday he and his players were scared that a loss for the home team might lead to stadium violence, but amid heavy security, attendance was low and the match passed without incident.
The Comoros, one of the continent's smallest countries, scored a come-from-behind 2-1 win away over Gambia to qualify from Group A and go to the finals for the second time after their giant killing appearance at the 2021 edition in Cameroon.
Myziane Maolida scored the last-gasp winner.
Zambia's 1-0 win over holders Ivory Coast in Ndola also put them into the finals as Kennedy Musonda scored two minutes before half-time. The Ivorians had already qualified from Group G.
Zimbabwe had been barred from the last edition of the continental championship after government interference in the running of their association led to an 18-month FIFA suspension, but bounced back to book their place despite a 1-1 home draw with Kenya.
Scotland-based attacker Tawanda Maswanhise had Zimbabwe 1-0 ahead before half-time of the Group J match played in Polokwane, South Africa, because Zimbabwe do not have a stadium that meets the Confederation of African Football's standards for international competition.
Kenya had to win to keep alive their hopes and pulled a goal back in the 52nd minute through Jonah Ayunga, but could not find the all-important second.
Hosts Morocco are also competing in the qualifiers and beat Gabon 5-1 away in Franceville with a double from Brahim Diaz making it five wins out of five in Group B.
Egypt's 1-1 draw earlier in the Cape Verde Islands saw them drop their first points in Group C.
Had Botswana beaten Mauritania, they would have gone through with Egypt from the group but had their hopes dashed in a 1-1 draw.
In Group K, South Africa beat Uganda 2-0 away in Kampala to take over at the top of the table from their hosts. Both countries had already qualified.
There are five more places to fill for the finals in Morocco, which kicks off in December next year. They will be decided between Saturday and Tuesday when the qualifying competition is completed.
