The seven-time AFCON champions took second place in Group D behind Nigeria, who defeated them in their opening game of the campaign, and look likely to face the Ivory Coast in the last 16.
Sudan goalkeeper Mohamed Mustafa did well to deny Mostafa Mohamed but Abdelmonem got the better of him with a powerful header from the edge of the six-yard box following a corner in the 35th minute.
Mohamed Salah was unable to finish off a mazy run in the 60th minute and Amr El Soleya failed to make the most of a neat lay-off from the Liverpool attacker shortly after.
Egypt's place in the knockouts was secured after Mohamed El-Shenawy saved Mohamed Abdel Raman's free-kick and got his head in the way of Mustafa Karshoum's follow-up, warding off the threat of a dramatic fightback from Sudan.
Despite dominating for large parts of the contest, Senegal were unable to break down Malawi's stern defence, with goalkeeper William Thole making a string of impressive saves.
However, after Robert Saiz hauled Mane down just outside the area, the Al-Nassr forward stepped up and curled home the winner in the sixth minute of second-half stoppage time.
The 2021 winners of the competition joined Burkina Faso in qualifying for the tournament that takes place in Morocco next year, with both sides on 10 points in Group L.
But in Group F, Ghana look set to miss the tournament for the first time since 2004 after slumping to a 2-0 defeat to Sudan at the Martyrs of February Stadium.
Despite the likes of Mohammed Kudus, Antoine Semenyo and Inaki Williams in their ranks, two goals in three second-half minutes from Ahmed Al-Tash and Mohamed Abdel Rahman did the damage.
Ghana remain winless in their four qualifying games so far and sit five points adrift of the top two, knowing they must beat both group leaders Angola and then Niger next month to have any chance of reaching the finals.
