Burkina Faso started more confidently, despite being without top scorer Alain Traore, and controlled the possession early on.
It was Togo who created the game's first meaningful opportunity though, when Serge Gakpe cleverly found Jonathan Ayite in the box, but the striker couldn't find a telling contact on the ball.
Burkina Faso responded, as Wilfried Sanou started causing Togo problems with his direct running and accurate crossing. They couldn't break down the Togolese though, and the teams went in at the break level.
Togo almost took the lead shortly after half time when Emmanuel Adebayor rose above two defenders and the goalkeeper to head towards an empty net; Saidou Panandetiguiri was there to clear off the line.
Both teams seemed to put more emphasis on attack thereafter, although neither could provide any real quality in the final third.
It was Togo who again created the best chance, with just 15 minutes left, Adebayor running clear of the Burkina Faso defence only to shoot straight at the goalkeeper.
There were few chances in the closing stages and the match headed into extra time.
The deadlock was finally broken after 105 minutes of play, and it was Burkina Faso who took the lead, when Jonathan Pitroipa found space at the near post to head home a corner.
Five minutes later the goalscorer was taken off for a defender, as Burkina Faso looked to see out the final minutes.
It proved to be a good decision as they won the game and will now face Ghana in the semi-finals.