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.
