Goalkeeper Fabrice Ondoa – the back-up stopper for Sevilla's B team – was the unlikely hero with the save, allowing substitute Vincent Aboubakar to hit the winning kick, leaving Mane absolutely distraught.
The defeat will provide a nasty sense of deja vu for Senegal head coach Aliou Cisse, who – as captain – missed the decisive penalty against Cameroon in the 2002 final.
Senegal are still waiting for a first major trophy, while Cameroon are just two steps away from winning their first title since that success 15 years ago.
Cameroon will play DR Congo or Ghana in Thursday's semi-final.
A quiet first half produced few clear opportunities, with Cameroon captain Benjamin Moukandjo seeing a long-range strike deflect over the crossbar.
Senegal had the best chance of the half when Keita Balde's cross was only half-cleared by Adolphe Teikeu, with the onrushing Cheikhou Kouyate's looping header just too high on the follow-up.
The Indomitable Lions almost got a fortuitous opener when Moukandjo's attempted cut-back deflected towards goal off defender Kalidou Koulibaly, but goalkeeper Abdoulaye Diallo reacted quickly.
Kouyate headed Kara Mbodji's free-kick off target early in the second period, before Senegal came even closer with the match's first shot on target.
Mane created the chance with a great run down the right, but Mame Biram Diouf's header was kept out at close range by Ondoa, who was then strong to prevent Keita from heading in the rebound.
Diouf, who hit back at criticism of his AFCON performances ahead of the game, was withdrawn by Cisse with 26 minutes remaining, Moussa Sow replacing him.
Keita tested Ondoa with a fierce long-range drive, but Cameroon almost grabbed a shock lead, Diallo making an excellent one-handed save from Moukandjo after Christian Bassogog's shot had fallen into his path.
Ambroise Oyongo struck the side-netting as Hugo Broos' side continued to pose a threat on the break, but Senegal could have had a late winner – Ondoa saving from Kouyate before Mane poorly missed the target from the rebound.
Senegal pressed hard for a winner, but Ondoa made another key stop from Sow as the tie moved into extra time.
Cameroon created the best chance of the additional period when a slick passing move ended with Jacques Zoua somehow failing to beat Diallo after being played in by fellow substitute Aboubakar.
Senegal, meanwhile, saw Keita blaze over from Saliou Ciss' cross as the game went to penalties.
Both sides netted their first four penalties, before Mane's effort was somehow saved by a combination of Ondoa's hand and foot, allowing Aboubakar to seal victory.