Mohamed Abdelmonem scored the match’s only goal, heading home Abdallah El Said’s corner for Pharaohs at the 35th minute.
Sudan could not score, with Egypt coming close to scoring a second goal through a Mohamed Salah effort that was well-saved in the second half by Ali Abu Eshrein.
Egypt will take on the winners of Group E Wednesday, 26 January.
They were three points behind Group D winners Nigeria, who defeated Guinea-Bissau by 2-0.
Sudan was champion in 1970. They played in their first major tournament in 2012 and finished third.
Egypt cruise to Yaounde to win
Egypt has been crowned seven-time Nations Cup winners. They have reached the knockout stage in five of six previous appearances at the Nations Cup.
They knew that a draw would secure their progress, while victory was what Sudan needed to stay alive.
Carlos Queiroz’s team dominated the match from the start, with Mostafa Mohamed’s forward kicking a goal past Mustafa, Sudan’s goalkeeper.
Once the Pharaohs had taken the lead, they continued to control proceedings with Mustafa equal to another Mostafa Mohammed effort just before the half-time break.
Liverpool forward Salah was also close to scoring, forcing Sudan’s substitute goalkeeper Abu Eshrein to make another great save with a low shot just after 58 minutes.
Salah set up Amr El Solia shortly after, but the midfielder couldn’t make a reasonable effort from close range.
In the game’s final stages, Sudan attempted a series of half-chances, but Egypt prevailed to take all three points.
