Zambia, who will face Nigeria in the last eight, finished in a three-way tie in the group but came out on top by virtue of the number of goals scored against the other three teams.
They were level on points with Cameroon and Gabon and also tied on goal difference but in a mini-league between the trio had scored four goals to Cameroon's three and Gabon's two.
Gabon were eliminated despite upsetting Cameroon in the group's opening game last week and also drawing with Tunisia.
James Chamanga'ssimple tap-in saw Zambia extend their lead just after the hour when he was left unmarked to receive Jacob Mulenga's square pass with Gabon's defence out of position.
"People were laughing at our chances and all the betting had us as the worst team here but today we proved we are good enough to reach the quarter-finals," said Zambia's youthful French coach Herve Renard.
"We thought we had qualified but then they told us no. It is heartbreaking but this is what sport is all about," said captain Daniel Cousin.
Cameroon and Tunisia drew 2-2 in the group's other match in Lubango on Thursday.
