The Elephants conceded to a Mohamed Aboutrika header in the 18th minute but got back into the game after the Gunners attacker converted a penalty.
Lacina Traore's goal then completed the turnaround before Gervinho grabbed his second with a tap-in just after the restart.
Mohamed Nagui pulled a goal back for the Pharaohs on the hour mark but it proved to be a mere consolation as Didier Ya Konan restored the two-goal advantage eight minutes from time.
Ivory Coast, which is seeded top of Group D, will play its first AFCON game against Togo in Rustenburg on Jan. 22.
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