An own-goal from Edmond Tapsoba and second-half strike from Lassine Sinayoko were enough for the Eagles to win the round-of-16 game, the last match of the tournament to be played in Korhogo.
Mali will next play Ivory Coast in Bouaké on Saturday, when the home team can count on supporters whose belief has been restored after beating defending champion Senegal on Monday.
Burkina Faso, which has repeatedly gone close to winning its first Africa Cup title in recent years, will have to prolong its wait after a campaign that never really sparked into life. The Stallions edged Mauritania 1-0, then drew 2-2 with Algeria, before losing their final group game 2-0 to Angola.
It was a bad start for Burkina Faso when Mali’s Amadou Haidara hit the post with a header and the ball rebounded off Tapsoba’s foot into his own net in the third minute.
Mali missed good chances to score before Sinayoko made it 2-0 by shooting between the goalkeeper’s legs in the 47th.
The Stallions were given a lifeline six minutes later when Kiki Kouyaté was penalized for hand ball. Bertrand Traoré scored from the spot to make it 2-1 in the 57th, finally giving his team the confidence to push for more.
Issoufou Dayo thought he’d equalized in the last minute but he had strayed offside before heading in a free kick.
World Cup semifinalist Morocco played South Africa later Tuesday for the last quarterfinal spot.
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