Veteran goalkeeper Essam El Hadary proved Egypt's hero, saving Bertrand Traore's spot-kick to secure victory.
In normal time Mohamed Salah opened the scoring for Egypt when he curled a superb shot into the top left corner.
Burkina Faso became the first side to score against Egypt this tournament when Aristide Bance chested down Charles Kabore's cross and volleyed in.
The Burkinabe, who were the more adventurous and ambitious side throughout normal play, took an immediate advantage in the shootout.
Goalkeeper Herve Koffi, only 20 years old, magnificently pushed Abdallah El Said's spot-kick on to the post.
But he later turned from hero to villain when he stepped up to take his side's fourth penalty and was unable to beat El Hadary - who at 24 years his senior is the oldest Nations Cup player in history.
El Hadary's experience - he now has a chance to win his fifth African title - proved vital as he then saved Bertrand Traore's effort to send Burkina Faso home.