Mane, Africa's most expensive player, was denied by Fabrice Ondoa, Vincent Aboubakar hitting the winning penalty.
Much fancied Senegal had a great chance to win it in normal time but Moussa Sow volleyed wide from close range to leave the game scoreless after 120 minutes.
Cameroon are four-time winners of the tournament.
The result means Mane is likely to make a swift return to his club Liverpool, who suffered a surprising defeat by Wolverhampton Wanderers in the FA Cup fourth round on Saturday.
There were striking similarities to this game and 15 years ago, when Cameroon and Senegal met in the 2002 final in Mali.
On that occasion, Cameroon beat Senegal 3-2 on penalties after a goalless 120 minutes.