The Stade Rennais winger nodded home after 105 minutes to guarantee the Stallions equal their best-ever finish at the tournament, after finishing fourth on home soil in 1998.
On a bone-dry surface in Mbombela Stadium, Burkinabe right-back Mohamed Koffi let fly from distance early-on but his shot was safely gathered by Kossi Agassa.
After a nervy opening quarter-hour for both sides Togo nearly took the initiative as Serge Gakpe burst free on the right, only for Jonathan Ayite to miscue his pull-back.
Burkina Faso were lacking end-product from their forwards too – missing three-time tournament goalscorer Alain Traore – with Wilfried Sanou drilling a shot into the dusty ground and wide minutes later.
Tottenham Hotspur striker Emmanuel Adebayor cut an isolated figure throughout the first-half and just before the break his dribble was expertly shepherded into touch by Bakary Kone.
But the Sparrow Hawks skipper almost provided a touch of class within seconds of the restart as Saidou Panandetiguiri hooked his goal-bound header off the line.
Chances remained few and far between, though Ayite showed flair to skip down the Stallions’ flank and force a corner – which centre-back Vincent Bossou nodded wide.
Into the last 20 minutes, a Togo set-piece was knocked down for substitute Prince Segbefia who skewed wide a golden opportunity to send his team to their first-ever Afcon semi-final.
The game began to liven up and a Stallions penalty claim was waved away as Prejuce Nakoulma was brought down, while the forward nearly turned provider for Pitroipa.
Adebayor then powered forward again – but Daouda Diakite parried his shot away – and Nakoulma continued to trouble the Sparrow Hawks’ defence, though his chip could not find the net.
Both teams were content to let the final minutes peter out for extra-time and quickest out of the blocks were Burkina Faso, as Agassa held-on to Abdou Traore’s strike.
And the Stallions made their pressure pay when an unmarked Pitroipa, peeling off the front post, looped a header over Agassa from Kabore’s outswinging corner.
In desperate search of an equaliser, the Togolese could not find space to pepper Diakite’s goal.
Burkina Faso are now only one game from the final, but must first overcome hot favourites Ghana on their return to Nelspruit on Wednesday.
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