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Finalist in 2013, Burkina Faso does not look like threatening to go that far on this evidence, with Ethiopia unfortunate not to claim all three points.
Ethiopia striker Getaneh Kebede saw a bending effort kept out of the top-left corner by Sofiane Ouedraogo in the 10th minute.
Cameroon held after stunning Cape Verde equaliser
It had four shots on target in the first half but it was Burkina Faso who had the only one to find the net, Cyrille Bayala lofting over Teklemariam Shanko after latching on to Adama Guira's superb chipped pass in the 24th minute.
Kebede was then denied again by Ouedraogo from close range, but he eventually got his reward for an impressive performance from the penalty spot.
Steeve Yago was adjudged by the VAR to have handled a free-kick in the area and Kebede coolly stroked into the bottom-left corner from 12 yards seven minutes into the second half.
But the draw proved enough to send Burkina Faso through as Cape Verde – whom it beat in its previous encounter – also drew 1-1 with group winner Cameroon. Ethiopia goes home with just a point to its name from only its second AFCON appearance since 1982.
