Jonathan Pitroipa headed in the only goal of an otherwise tedious contest seconds before the half-time whistle in extra-time.
The Rennes forward was one of the few creative influences and deservedly provided the decisive moment in a match that was hampered by a sandy surface at the Mbombela Stadium.
Burkina Faso have only once previously reached the last four, when they hosted the tournament in 1998, but had otherwise failed to register a win in the African finals before arriving in South Africa.
Paul Put's side will go into Wednesday's semi-final against Ghana, at this same venue, as underdogs although they will at least have experience of playing on a tricky surface that troubled both sides.
Despite that, Burkina Faso - ranked 92 on FIFA's world rankings - were just about deserved winners and could have settled it earlier when they were declined what appeared a clear penalty on 76 minutes.
Prejuce Nakoulma went down under a tangle of legs with Vincent Bossou, only for the referee to wave his claims away.
Togo's attacking forays were rare, with star striker Emmanuel Adebayor conspicuously absent, although the Tottenham man could have had a penalty of his own moments later when Bakary Kone hastily lunged in.
Adebayor instead opted to keep his feet and it took goalkeeper Daouda Diakite to block his tight-angled shot after quickly leaving his line.
Togo were playing their first quarter-final at a major tournament and showed signs of stage fright, with only a scuffed Floyd Ayite effort providing a sign of their threat before half-time.
In an otherwise forgettable first 90 minutes, Pitroipa at least crafted a couple of half-chances.
Late in the second half he and Nakoulma combined down the left but, after some pinball in the area, Pitroipa scooped a shot on to the top of the netting.
With the match sent into extra-time, it appeared both sides were waiting for penalties until Pitroipa eventually found the decisive touch.
Charles Kabore's corner found him unmarked at the near post and, with goalkeeper Kossi Agassa starting to leave his line to try and claim the ball, Pitroipa expertly guided his header into the net off the crossbar.