It took a late 89th minute strike from from substitute Abdalla El Said to break the deadlock from the hard fighting Ugandan side.
The victory means that Egypt can still qualify from the Group D with four points from two matches. The Pharaohs drew the first match 0-0 against Mali.
Ghana are currently toping the Group D standing after defeating Mali by a lone goal by Asamoah Gyan in the 21st minute of the game played earlier on Saturday. Ghana’s Black Stars now have six points having defeated Uganda 1-0 in their first match.
Egypt currently facing goal-keeping crisis with two out of the three goalkeepers sidelined with injury has to put faith in the veteran goalkeeper Essam El Hadary to save the team from early exit.
Ghana is the second team to qualify for the quarter-finals after Senegal reached the last eight from Group B.