The Confederation of African Football's referee's review committee overturned Pitroipa's ban after Tunisian referee Slim Jdidi told CAF he made a mistake with the second yellow card shown to the player for simulation.
Jdidi has since been suspended by African soccer's governing body for his handling of the match which surprise package Burkina Faso won 3-2 on penalties after the game ended 1-1 following extra time.
Pitroipa, 26, who had already been booked for deliberate handball, went to ground three minutes before the end of extra time inside the penalty area but TV replays clearly showed he had been fouled in the 117th minute incident and did not dive.
A senior CAF official told Reuters: "The referee wrote the letter to the review committee saying he had made a mistake. The review committee examined footage of the incident and agreed Pitroipa had been fouled.
"It asked the disciplinary committee to verify its decision which the disciplinary committee is entitled to do under the terms of CAF's rules and regulations."
Earlier on Friday, CAF president Issa Hayatou had indicated Pitroipa's ban would be overturned when he told reporters: "Everyone realised that this referee did not officiate well.
"The referee admitted his error - he recognised that he had got it wrong."
Pitroipa, who plays for Stade Rennes in France, has been highly influential for the Burkinabe on their route to the finals, scoring twice including the winner in the 1-0 quarter-final extra time victory over Togo.
Television pictures showed him utterly distraught in the tunnel after his sending off, but at least CAF have now ruled correctly by overturning the ban.
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