The Red Devils had to wait until the 87th minute to get a well-deserved winner when Algerian midfielder Ahmed Kendouci intercepted the ball in midfield to set up El Shahat in the area who slot home from close range.
The 31-year old winger has repaid his club's faith after inking a new deal that will keep him at Ahly until 2026.
Marcel Koller's men enjoyed a large ball possession of more than 70 percent but couldn't capitalize on domination.
Suez SC keeper Mahmoud Koko made some impressive saves including a penalty kick by Rami Rabia in the 53rd minute to keep his team in the game until the dying minutes.
Ahly will face Dakhleya in the round of 16.
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