The defending champions stayed on course for a record-breaking third successive title and took revenge on the Algerians who beat them in a World Cup play-off last November.
The much-anticipated clash between the two bitter rivals deteriorated before half-time and was over as a contest long before the final whistle.
Egypt were 1-0 ahead at the interval after Rafik Halliche had given away a penalty converted by Hosni Abd Rabou in the 39th minute.
The tackle brought out a second yellow card inside eight minutes for the Algeria defender, leaving his side a man down with some 50 minutes left to play.
Egypt overwhelmed Algeria in the second half but only made sure of their progress once Mohamed Zidan produced a stunning left-footed finish in the 65th minute.
WILD LUNGE
Six minutes later Algeria were down to nine men when a wild two-footed lunge from Nader Belhadj landed him a straight red card and a possible two-match ban, possibly ruling him out of the opening game of the World Cup.
Egypt toyed with their opponents after that, slowing the game down to pedestrian pace and picking it up again to allow substitutes Mohamed Abdelshafi and Mohamed Nagui to add late goals.
Abdelshafi scored from a tight angle after a strong run down the left in the 80th minute and Nagui finished from close range in stoppage time, his fourth goal of the tournament making him its leading scorer.
Goalkeeper Faouzi Chaouchi had also been sent off for a second yellow card, after a wild kick at an advancing Egyptian player with four minutes left.
He was fortunate not to have been sent off earlier when, disputing Egypt's penalty, he grabbed the Benin referee Bonaventure Coffi Codjia by the collar and head-butted him.
Egypt and Ghana will meet in their eighth Nations Cup final appearance each. Algeria will play Nigeria in Saturday's third place play-off in Benguela.
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