Victory for Senegal set up a final against Morocco, who secured a 4-2 penalty shootout victory over Nigeria in the other semi-final.
Senegal's win was thoroughly deserved, after they dominated Wednesday's match, with Egypt, featuring superstar Mohamed Salah who was Mane's former clubmate at Liverpool, not having any shots at goal or even forcing a corner before they conceded.
Senegal found it tough, however, to break down a resolute Egypt defence and it was only a fortuitous deflection that set up Mane's chance.
Yet the decisive shot from the edge of the area by Mane, who plays his club football in Saudi Arabia these days after his wonderful strike partnership in the Premier League with Salah, was worthy of winning any match.
Lamine Camara's effort from the edge of the area was blocked, but it fell to Mane nearby and he wasted no time bulleting the ball along the ground with a grass-cutting shot that gave Egypt goalkeeper Mohamed El Shenawy no chance.
Senegal probed throughout the game as they tried to force an opening, but opportunities were rare.
Nicolas Jackson, restored to the team, fired a powerful effort over the top in the 19th minute, followed by shots from Habib Diarra and Pape Gueye that provided El Shenawy with routine saves.
In the second half, Senegal continued to dominate possession but were again restricted to speculative efforts from range before Mane's goal.
After they scored, it finally prompted Egypt to push forward with three strikers brought on in a late, and desperate, bid to get back into the game.
Defeat ended Salah's hopes of securing a first title with his national team, with the Liverpool star having little impact on the game. He had twice been a losing finalist at the Cup of Nations.
Senegal lost captain Kalidou Koulibaly to a groin injury midway through the first half, but not before he had been booked for a foul on Omar Marmoush, which ruled him out of the final.
Diarra, who plays for Sunderland in the Premier League, was also booked for a second successive game and is suspended for Sunday's decider.
In Rabat, Yassine Bounou saved two penalties and Youssef En Nesyri netted the decisive spot kick as hosts Morocco secured a 4-2 shootout victory over Nigeria following their 0-0 draw in their tense semi-final.
The 120 minutes before the shootout had few clear-cut chances for either side, but it was Morocco who created the greater opportunities, though they were denied by some fine saves from Nigeria goalkeeper Stanley Nwabali.
Morocco, seeking their first continental title in 50 years, will face 2021 winners Senegal in Sunday's decider in Rabat, with Nigeria to take on Egypt in the third-place playoff on Saturday.