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Burkina Faso got off to the better start in Ebebiyin and had a chance inside the opening 10 minutes when the player of the tournament from two years ago, Jonathan Pitroipa, headed wide.
Congo's brightest player in the first half was Thievy Bifouma, but he couldn't unlock the Burkina Faso defence, shooting wide and failing with a penalty appeal.
Ferebory Dore squandered a couple of openings at the start of the second half for Congo before the group leaders did take the lead when Dore crossed for striker partner Bifouma to slot home.
Burkina Faso had to win to go through and they gave themselves hope of a late fightback when Aristide Bance fired home in the 86th minute.
It wasn't to be, though, as Congo went up the other end straight away and sealed their place in the last eight through Fabrice Ondama N'Guessi.
They are joined in the quarters by tournament hosts Equatorial Guinea, who beat Gabon 2-0 in Bata.