The Pharaohs needed extra-time to see off the Cheetahs at Stade Adrar on Monday after Jodel Dossou (83') cancelled out a 69th minute opener from Marwan Attia.
Yasser Ibrahim fired home after 97 minutes, and Mohamed Salah sealed the result with his goal on 124 minutes.
Egypt will now play AFCON holders Ivory Coast, who defeated Burkina Faso 3-0 in their first knockou match.
Reflecting on the game, Hassan explained that there are no easy games at AFCON.
He told CAFOnline: "It was a very difficult match. Before the game, I said there are no easy teams, and Benin were a tough opponent.
"We work to analyse every opponent in order to adapt our game. Egypt is a great football team and I want to make my people happy.
“I trust my team and my staff, especially the medical staff, to ensure good recovery before the next match.”