Egypt's captain, starting his first game after four successive matches on the bench at Liverpool, fired home a left-footed effort in the 91st minute to earn the seven-time champions a late victory after Zimbabwe had stunned them by going ahead in the Moroccan coastal city Agadir.
Hossam Hassan's side laid an early siege to Zimbabwe's goal, but it was the underdogs who netted first through Prince Dube in the 20th minute.
It was left to Egypt's Premier League contingent of Omar Marmoush, who equalised in the 64th minute, and talisman Salah to see them to a last-gasp victory.
It was as much as they deserved, breaking a run of six successive draws over the last two editions of the tournament.
"We created many chances without being able to score early, but in the end everything went well," Manchester City's Marmoush said.
"We kept a good mindset and finished the match strongly. We will learn from everything that happened in tonight's game."
Earlier on Monday, Lyle Foster gave South Africa a winning start by netting the second goal in a hard-fought 2-1 victory over Angola.
Oswin Appollis opened the scoring in Marrakech for Bafana Bafana with a low strike in the 21st minute, but midfielder Show equalised 14 minutes later when he deflected Fredy's free kick from the wing inside the near post.
Tshepang Moremi had a goal ruled out for offside after a VAR review and Mbekezeli Mbokazi struck the crossbar with a fierce strike as South Africa kept pushing.
Angola coach Patrice Beaumelle refreshed his attacking line-up in the 76th minute but it was Foster who curled the ball beyond Hugo Marques in the 79th.
And in Casablanca, Patson Daka scored in added time for 2012 champions Zambia to grab a 1-1 draw against Mali.
Mali missed a penalty before the break when Willard Mwanza saved El Bilal Toure's effort – the second saved spot kick in as many games at the tournament.
Lassine Sinayoko broke the deadlock around the hour mark, but a Daka header earned Zambia a point.
With Reuters.
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