Four-time champions Cameroon will face hosts Ghana in Thursday's semi-final after an extra-time finish from Stephane Mbia knocked out Tunisia.
Cameroon celebrate their progress through to the semi-finals
Mbia knocked in Jean Epalle's flick on in the 92nd minute, after his header in the first half gave Cameroon the lead.
Geremi's free-kick from close to 30 yards extended the Indomitable Lions' lead before Tunisia's Chaouki Ben Saada hit back with a free-kick of his own.
Yassine Chikhaoui struck from close in on 81 minutes to force extra-time.
The quarter-final in Tamale was a fascinating game as fine goals and a never-say-die attitude from both sets of players forced tactical changes from old-hands Roger Lemerre and Otto Pfister.
Stephane Mbia puts Cameroon in the lead
Cameroon narrowly deserved the win, but Lemerre's Tunisia showed great composure and ability throughout to force the Indomitable Lions to play 120 minutes before they could claim the victory.
Lemerre started with Chikaoui and Francileudo Dos Santos leading his attack but it was Cameroon that had the first chance of the match.
Samuel Eto'o worked hard to keep the ball in play from a long pass, Geremi then jinked and crossed to the far post where Jean Makoun headed wide from ten yards.
Though much of the early play was scrappy and dogged with fouls, Cameroon, spear-headed by Eto'o, were looking dangerous on the break.
The breakthrough soon followed when Arsenal's Alexandre Song swung a deep-cross to the far post allowing an unmarked Mbia to head into an empty net on 18 minutes.
Geremi added to the lead ten minutes later when he nonchalantly curled in a direct free-kick from close to 30 yards, over the wall and into the right-hand corner of the goal.
Tunisia's game plan had been undone and Cameroon were threatening to run riot, until Ben Saada showed he could compete with Geremi when he whipped in a free kick of the highest quality from 25 yards to confound Idriss Carlos Kameni and give his side a foothold in the game.
Lemerre's men were in the ascendancy when Dos Santos turned to rattle the bar with a rasping shot from inside the area with four minutes remaining in the half.
Chikhaoui's late finish forced the game into extra-time
Ben Saada pounced on the rebound and hit a first-time shot only for Kameni to show fantastic reflexes to save low down.
Tunisia started the second half brightly when the deceptively quick Chikaoui burst through the Cameroonian back four and forced a desperate tackle from Atouba to prevent him from a one-on-one with Kameni.
A frenetic period followed from the Tunisians as the side from north Africa tried to force an uncomfortable pace on Cameroon.
But the Indomitable Lions remained unfazed and were happy to sit back and soak up the pressure while trying to capitalise on the kind of breakaway chances that fell to Eto'o on 71 minutes, when only a superbly timed tackle from Rahdi Jaidi prevented the lone striker from causing further damage.
Tunisia seemed to have run out of steam with ten minutes remaining, until persistence on the right flank played in Chikaoui who fizzed a first-time shot into the goal.
Cameroon had a glorious chance to steal a late win when Mohamadou Idrissou crossed to the far post only for Epalle to arrive too late to apply the finish and prevent the game from going into extra-time.
But within minutes of the restart Mbia reacted swiftly in the area to Epalle's flick on, with a crisp finish inside the near post to reinstate Cameroon's lead.
Tunisia would still not lay down though and a succession of corners and half chances had Cameroon's fans biting their nails until the very end.
Tunisia: Kasraoui, Haggui (Ben Fredj 39), Jaidi, El Bekri, Felhi, Nafti (Jemaa 71), Mnari, Traoui, Ben Saada, Chikhaoui, Santos (Chermiti 86).
Subs Not Used: Mathlouthi, Nefzi, Abdi, Ghezal, Meriah, Mikari, Zaiem, Zouaghi, Ben Dhifallah.
Booked: Nafti, Jaidi.
Goals: Ben Saada 35, Chikhaoui 81.
Cameroon: Kameni, Song, Bikey, Atouba (Tchato 108), Geremi, Emana (Epalle 62), Makoun (Binya 65), Song Billong, Mbia, Eto'o, Idrissou.
Subs Not Used: Mbarga, Hamidou, Angbwa, Essola, M'Bami, N'Guemo, Nkong, Tomou, Job.
Goals: Mbia 19, Geremi 27, Mbia 92.
Ref: Koman Coulibaly (Mali).