The loss ended Pyramids' title defence despite a 1-1 draw in the first leg in Rabat. The Egyptians won their first African Champions League crown last June, beating South Africa’s Mamelodi Sundowns.
Rida Slim put the visitors ahead in the ninth minute at Cairo's 30 June Stadium before Mohamed Rabie Hrimat doubled the lead with a 54th‑minute header.
Fiston Mayele halved the deficit in the 62nd minute but the Egyptians could not find the equaliser that would have sent the tie straight to penalties as FAR Rabat held firm.
"This is a historic win and a historic qualification for the club," forward Youssef El Fahli told beIN Sports. "We have the determination to fight for the title this season and, God willing, we'll bring home the club's second continental crown."
FAR Rabat will face fellow Moroccans RS Berkane or Sudan's Al Hilal in the semi-finals, hoping to move a step closer to a second continental crown after winning the African Cup of Champions Clubs in 1985 when they beat AS Bilima (now AS Dragons) of then Zaire, now Democratic Republic of Congo.