Egypt were unlucky not to find a breakthrough in 120 minutes, having spurned several clear-cut chances as a jaded-looking Ivorian side failed to keep pace with the record seven-time African champions.
Keeper Mohamed Abou-Gabal, who replaced Mohamed El-Shennawi just before the end of regulation time after the Ahly goalie was injured, proved an unlikely hero, producing a superb one-handed save to block Eric Bailly's third spot-kick.
Salah then stepped up for Egypt's fifth effort, which he powerfully fired into the bottom corner to send keeper Badra Sangare the wrong way and spark wild celebrations among his teammates, many of whom are tasting Nations Cup action for the first time.
Although Cote d'Ivoire still managed to mount some threats, they looked largely toothless with Egypt's backline, marshalled by the rookie but solid defender Mohamed Abdel-Moneim and the experienced Ahmed Hegazi, nullifying the threats of the likes of Sebastien Haller and Nicolas Pepe.
At the other end, Egypt launched some breakaways which, had it not been for some poor finishing, could have settled the tie before it went to extra time.
Egypt continued their habit of eliminating Cote d'Ivoire in the Nations Cup, having defeated the Elephants en route to four out of their last five triumphant campaigns.
They will face a mouthwatering quarter-final clash against Morocco, who came from behind to beat Malawi 2-1 after producing a vivid attacking display on Tuesday.
Cautious approach
Egypt's cautious approach appeared to work well in the first half, with Cote d'Ivoire restricted to a single goal-scoring chance and the Pharaohs looking dangerous on the break.
Winger Omar Marmoush created Egypt's best chance after 17 minutes when a sloppy pass by defender Simon Deli was intercepted and the Stuttgart man's dipping shot came back off the bar.
Four minutes later, Salah had a half-volley on the edge of the area tipped over by keeper Badra Sangare.
Cote d'Ivoire were unlucky to lose burly midfielder Franck Kessie to injury but they improved in the latter stages of the first half following a slow start, going close six minutes before the break.
A rare defensive lapse saw Ibrahim Sangare meet a cross from the right with a bicycle effort that Egypt keeper El-Shennawi did well to keep out with a fine one-handed save.
At the other end, Egypt's lone striker Mostafa Mohamed had a couple of half-chances but his finishing touches let him down.
In the second half, Egypt continued where they left off, with midfielder Amr El-Sulaya missing a sitter on 52 minutes when he fired high over with the goal at his mercy after some good work from Salah, who cut inside from the right and slipped a pass to the unmarked Ahly midfielder.
A brief period of Ivorian pressure could have resulted in a goal against the run of play though when Ibrahim Sangare flicked a corner to Haller, whose close-range header was tipped over by El-Shennawi in the 70th minute.
The towering keeper also smothered substitute Wilfried Zaha towards the end, only to pull a hamstring and make way for Abou-Gabal, who did not disappoint.
Abou-Gabal produced a superb reflex save to push away a curler from Sangare in the first half of extra time while Egypt substitute Mahmoud Trezeguet wasted a couple of good chances at the other end.
The match then went to penalties, with Egypt converting all their five efforts to deservedly go through and continue their bid towards a record-extending eighth crown.
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