A defensive mix up gifted Burkina Faso the lead, as defender Rudinilson Silva headed past onrushing goalkeeper Jonas Mendes and into his own net.
On-loan Ajax forward Bertrand Traore doubled the advantage with a composed left-footed finish after the break.
Cameroon also went through as group runners-up after a goalless draw with Gabon that saw the hosts eliminated.
Guinea-Bissau, making their Africa Cup of Nations debut in this tournament, looked the more likely to open the scoring, before handing Burkina Faso the lead.
Rudinilson’s header looked to have crossed the line, but Prejuce Nakoulma thumped in to make sure after Guinea-Bissau attempted to scramble it away.
The dangerous Piqueti went closest to levelling, but Burkina Faso keeper Koffi Kouakou was able to push the winger’s low strike wide of the far post.
Juary Soares could have equalised in the second half when a corner found the Guinea-Bissau defender unmarked at in the six-yard box, but Abdou Traore threw himself in front of the goalbound shot.
Burkina Faso immediately went down to the other end to increase their lead, with Nakoulma setting up Traore, on loan at Ajax from Chelsea, to slide a finish beyond Mendes.