The first leg result ended a 38-match unbeaten home run by the Pharaohs since qualifying was introduced in 1965 and leaves them in danger of elimination after the teams clash again on 30 June in Bangui.
After Mohamed Zidan put the home team ahead on ten minutes, his blunder at the other end of the field allowed Hilaire Momi to equalise, before the visitors had Salif Keita sent off for a second caution.
Mohamed Salah atoned for several squandered scoring chances by putting Egypt ahead again three minutes into the second half but the home defence was caught napping just past the hour mark.
They reacted slowly after fouling Foxi Kethevoama, whose quick free-kick put Momi through for his second goal, and David Manga struck the winner for the Wild Beasts with 21 minutes left.
Egypt are now facing the grim prospect of missing a second consective Cup of Nations tournament after finishing last behind shock group winners Niger, South Africa and Sierra Leone in the 2012 qualifying pool.
Hassan Shehata, who guided the Pharaohs to three consecutive African titles from 2006, quit before the end of that qualifying campaign and was replaced by former USA coach Bob Bradley.
All seemed well for the American when his team defeated Mozambique at home and Guinea away in 2014 FIFA World Cup™ qualifying this month as the Pharaohs seek a third appearance at the finals.
Algeria, meanwhile, became the first country to qualify for the final elimination round this September and October by outplaying Gambia 4-1 in Blida after building a 2-1 first-leg lead four months ago.
Foued Kadir and Islam Slimani had the Desert Foxes two goals ahead within six minutes, Saidhou Gassama pulled one back before half-time, only for Slimani and El Arabi Soudani to score further goals for the home side.