Salah scored the decisive winner, while goalkeeper Abougabal, who replaced the brilliant first choice El Shenawy, saved Eric Bailly's no-look kick to send the Pharaohs to the quarterfinals.
The match itself was a game of two halves as Egypt started well in the first half and created the best chances.
Omar Marmoush rattled the Ivorian bar early in the first half with a superb effort from a distance, while Salah also had a shot tipped over the bar by the goalkeeper, Bandra Ali.
Ivory Coast lost star midfielder, Franck Kessie, to injury in the first half, while Ibrahim Sangare had their best chance with a bicycle kick.
In the second half, substitutes, Trezeguet and Wilfred Zaha went closest for both sides and the game entered extra time, with Trezeguet wasting the best chance to win the game late on.
Egypt goes through and will play North African rivals Morocco in the last eight on Sunday.
Jesus the saviour as Equatorial Guinea continues impressive run
Equatorial Guinea continues to impress at the Africa Cup of Nations in Cameroon after sending favourites Mali home via penalties.
The round of 16 clash between the two ended goalless after extra time with Equatorial Guinea's 20-year-old goalkeeper, Jesus Owono saving two penalties during the shootout, with his low save to Falaye Sacko the decisive one.
Mali missed three spot-kicks through Massadio Haidara, Hamari Traore and Falaye Sacko, while Emilio Nsue and Pablo Ganet missed for Equatorial Guinea.
While the shootout provided dramatic talking points and dramatic end to the final game of the first knockout stages, the game itself also had some key moments in normal time.
Mali was awarded a bizarre penalty just before the first half break when Doumbia went on the floor following a challenge from Miranda in the 39th minute.
However, the VAR stepped in the save the day as the decision was rescinded. It was the closest either team came to breaking the deadlock in the first half.
In the second half, Mali also had the best opportunity to find the breakthrough when Brighton and Hove Alvin star, Yves Bissouma picked out Mohamed Camara with a superb pass but the forward blasted his effort in a rugby style from the 18 yard box.
Equatorial Guinea finally had a good chance of their own in the first half of extra time when Kouyate fouled Nsue in the box but the penalty appeals by the Malians was thrown out by the VAR.
Equatorial Guinea qualify for another AFCON quarterfinal and will face Senegal on Sunday.