The 44-year-old saved from opposite number Kouakou Herve Koffi and Bertrand Traore to seal a 4-3 victory on spot-kicks following a 1-1 draw in Libreville.
The Pharaohs, who had not conceded a goal en route to the last four, were second best for much of Wednesday's clash, but the seven-time champions still extended their unbeaten run in the competition to 24 matches.
Egypt took the lead against the run of play in the 66th minute through Rome forward Mohamed Salah's stunning strike, but Hector Cuper's side were breached for the first time in the tournament soon after.
Aristide Bance, who came off the bench to score in the quarter-final win over Tunisia, showed composure to control Charles Kabore's cross on his chest and deliver a cool finish from inside the box.
Burkina Faso – who have never won the AFCON – still looked the more likely when the game went to extra time, but failed to make it count and it came down to spot-kicks.
Koffi had looked set to grab the headlines when he saved brilliantly from Abdallah Said, who was first up, but he later saw his own attempt kept out and Bertrand Traore's failure proved decisive.
It was not until the 17th minute that the Pharaohs flexed their attacking muscles, with Trezeguet expertly cutting on to his right foot before sending a curling shot narrowly wide of Koffi's left-hand upright.
Paulo Duarte's side enjoyed a much greater share of possession in the first half, but their play in the final third was often rushed and wasteful.
Prejuce Nakoulma's powerful 25-yard strike was not lacking in ambition, though accuracy was an issue as it flew well over the crossbar 10 minutes before half-time.
Egypt almost snuck ahead before the interval when Kahraba's effort took a wicked bounce just in front of Koffi, who adjusted well to keep the ball out.
Bertrand Traore, who spoke before the game about his desire to impress Chelsea boss Antonio Conte, forced El-Hadary into action with a stinging drive from a set-piece early in the second half.
But it was opposite number Koffi who had to pick the ball out of his net, beaten by Salah's superb strike after he collected a lay-off from Kahraba, whose earlier booking ruled him out of the final.
It took only seven minutes for Burkina Faso to score a thoroughly deserved equaliser as Steeve Yago's back-heel teed up a cross for Kabore that was chested down and powered home by Bance.
El-Hadary's save from substitute Banou Diawara's miscued shot ensured the contest went to extra time, during which some last-ditch defending from Ahmed Hegazy denied Nakoulma a chance to shoot from close range.
Alain Traore was introduced and thrashed an off-balance shot over the crossbar as the game wound its way towards penalties.
Koffi's save to deny Said was remarkable, but his joy was turned into despair by another fine stop from El-Hadary after a run of six successful kicks.
Amr Warda then netted and when Bertrand Traore also fell victim to El-Hadary's ageless brilliance, Egypt were left to celebrate reaching yet another final while Duarte's men looked distraught, with Koffi among those in tears.