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 levelled when Aristide Bance chested down Charles Kabore's cross and volleyed in.
In doing so, they became the first side to score against Egypt this tournament.
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 soon experienced the other side of shootouts 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.
It was a dramatic end to a game that was cagey, thanks to Egypt's predominantly defensive approach, which had served them well and meant they had not conceded a goal going into the match.
Two moments of excellent football provided the breakthroughs for the teams - Salah's curling opener was sublime as was the chest control and volley from Bance that restored parity.
Otherwise the football was not quite of the highest standard, with Koffi largely a bystander.
While El Hadary was called on more often, he was relatively comfortable in keeping out shots from Prejuce Nakoulma and Banou Diawara.
Egypt's victory continues their remarkable success rate in Nations Cup semi-finals - they have now won their past six.
In clinching victory in Libreville they equal Ghana's record of appearing in nine finals.
And if on Sunday they beat the winner of Thursday's semi-final between Cameroon and Ghana, Egypt will extend their own record as the most successful Nations Cup side with an eighth title.