Pitroipa pulled away from his marker in the last seconds of the first period of extra time to head Charles Kabore's corner in off the underside of the bar to send Burkina Faso through to a meeting with Ghana back 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 in seven previous attempts, but he was unable to find the net with one effort cleared off the line and another well saved by Burkina goalkeeper Daouda Diakite.
Burkina's Belgian coach Paul Put dedicated the victory to the country's president Blaise Compaore who was celebrating his 62nd birthday, adding: "This is like a never-ending story. We are very happy and very proud.
"The pitch is hard and the conditions are difficult but it is like our home pitch now and I am looking forward to meeting Ghana in the semi-final.
"I don't have a crystal ball and cannot tell you what will happen but our objective was to reach the semi-finals and we have done that, and I am the happiest coach at this tournament."
Togo coach Didier Six was naturally disappointed at the result but praised his players for making it this far.
"If you make it into the quarter-finals you deserve to be there and this was a historic qualification for Togo as they have never been to this stage before," he told reporters.
"Overall, this has been a very good tournament for us. Togo has a lot of quality, a lot of good young players and a bright future ahead of them and I am very proud of my players tonight."
But while there some clever individual skills on display, the match itself was a poor one, littered by 53 fouls and with only seven attempts on target during the 120 minutes.
Whether it was the sandy pitch or the rarefied atmosphere of reaching the quarter-finals, 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 kick-off.
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
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