Jonathan Pitroipa pulled away from his marker at a corner in the last seconds of the first period of extra time to head in off the underside of the bar to put Burkina Faso through to the last four where they will meet Ghana in Nelspruit on Wednesday.
The match, on the hard, sandy pitch at the Mbombela Stadium, seemed destined to go to penalties after 90 minutes of largely uninspiring football, although both sides did have chances to win it in the closing minutes of normal time.
Togo's talismanic skipper Emmanuel Adebayor worked tirelessly for his side, who had never reached this stage before, but he was unable to find the net with one effort cleared off the line and another well saved by Burkina goalkeeper Daouda Diakite.
Whether it was the sandy pitch or the rarefied atmosphere of reaching the quarterfinals, both sides took time to settle but after a poor first half the match improved as a spectacle but there was still a lack of real quality in front of goal.
Burkina Faso, missing injured in-form striker Alain Traore who scored two superb goals in the 4-0 win over Ethiopia in the group stage, rarely worried Togo keeper Kossi Agassa, while Togo's forwards were also way off target.
Floyd Ayite missed Togo's best chance early chance, failing to connect with a mis-kick after 18 minutes.
Adebayor, a regular scorer in the Premier League over the years, was playing far deeper for Togo in the first half at least but even he struggled on the pitch he described as "a disgrace to the African continent" before the kickoff.
Playing in a more advanced role from the start of the second half though, he came close to opening the scoring in the 47th minute when Ayite surged forwards deep into Burkinabe territory before crossing wide to Serge Gapke.
Adebayor, anticipating Gapke's cross, outjumped two defenders and goalkeeper Diakite but although he did not get a clean header to the cross, the ball came off his back and was bouncing into the goal only for defender Mady Panandetiguiri to hook it clear just before it crossed the line.
Prince Segbefia, who replaced Ayite after 67 minutes, had a good chance to put Togo ahead six minutes later when the ball bounced perfectly into his path 10 metres out but he blasted it over.
The next opportunity was Adebayor's who went on a rampaging run in the 78th minute, evading a tackle, but Diakite made a good save from his angled drive.
Burkina substitute Prejuce Nakoulma then had a real chance to save everyone from another half-an-hour but over-elaborated on a jinking run through the defence towards Togo's goal and wasted his chance with a weak shot which Agassa blocked.
The match went into extra time with Pitroipa's header proving decisive in sending Burkina through to meet Ghana, who beat Cape Verde Islands 2-0 in their quarterfinal on Saturday. – Reuters