Christopher Katongo scored the only goal of a cagey match midway through the second half as Zambia finished top of Group A with seven points and pushed already-qualified Equatorial Guinea into second place with six.
Zambia will face the Group B runners-up in their quarter-final in Bata while Equatorial Guinea will meet the Group B winners in Malabo. Ivory Coast currently lead Group B and need a point against Angola on Monday to finish top.
For the first time in the tournament, the co-hosts included a locally-born player in their starting line-up as Jose Bokung was picked at left-back.
Equatorial Guinea's team is made up of Spanish-born players who qualify through their parents and naturalised players from other countries including Brazil, Nigeria and Cameroon. They started their previous two games with 11 foreign-born players.
The 15,000 capacity Estadio Nuevo de Malabo was full for the match, with hundreds more onlookers gathering outside the entrance to savour the atmosphere.
Fans inside were unusually subdued by African standards with no bands playing. Instead, most of the red-shirted fans blew plastic horns and banged inflatable batons provided by sponsors and there was even the odd vuvuzela, a rarity at the tournament.
The home side had the best chance of the first-half when Ivan Bolado cleverly worked an opening but was denied by Kennedy Mweene at the last minute.
Zambia broke through in the 67th minute when Chinese-based Katongo collected the ball from a throw-in and scored with a low shot from the edge of the penalty area which went just inside the near post.
Equatorial Guinea were agonisingly close to a quick equaliser when captain Juvenal Edjogo curled a free-kick narrowly past the upright.
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