The match finished 0-0 after extra time before Abo Gabal, who had replaced the injured Mohamed El Shennawy, pushed a casual effort from Ivorian defender Bailly onto the crossbar and Salah struck the winning penalty from his trademark long run-up.
Seven-time winners Egypt will now face north African rivals Morocco in an enticing quarterfinal at the Stade Ahmadou Ahidjo in Yaounde on Sunday.
It was a lively match at the Japoma Stadium in Douala in which both sides created enough chances to win the game, but also at times lacked quality in the attacking third at either end in another largely quiet outing for Egypt captain Salah.
Egypt are seeking their first continental title since 2010 having surprisingly fallen at the last-16 stage on home soil in 2019.
The Pharaohs, who have now progressed on all five occasions they have met the Ivory Coast in the knockout stages at the finals, reach the last eight having only scored two goals in their four matches.
Their opponents had been more fluent in attack in recent matches but came up against a stoic Egyptian defense that was organized and unyielding.
Egypt midfielder Omar Marmoush crashed a shot against the crossbar midway through the first half, before Salah’s goal-bound shot from the edge of the box was saved by keeper Badra Ali Sangare.
But perhaps the best chance fell at the other end when Ibrahim Sangare’s acrobatic shot was beaten away by El Shennawy in the Egyptian goal.
The latter also had to be smart to keep out an effort from Sebastien Haller on the stroke of halftime.
El Shennawy tipped over a close-range header from Haller, before he was forced off with a leg injury just before the end of the 90 minutes and replaced by Abo Gabal.
Egypt created a number of half-chances in extra time, but Sangare unleashed a curling effort that was superbly saved by the Egyptian keeper to send the game to penalties.