Angola lost 1-0 to Ghana in their quarterfinal tie in Luanda despite the support of a capacity 50,000-strong crowd, while the dreams of Didier Drogba and his Ivorian side faded in a dramatic contest in Cabinda.
Algeria twice came from behind to beat the Ivorian 3-2 in extra time to complete a remarkable recovery after losing their opening game at the tournament 3-0 to lowly Malawi.
Asamoah Gyan broke home hearts with a 16th minute winner as Ghana held Angola at bay and sent the host nation out.
Algeria looked to be on their way out Salomon Kalou scored for the Ivory Coast after just four minutes at Cabinda's Chiazi Stadium.
But Algeria provided increasing resistance after that and were worthy of an equaliser just before half-time after a defensive slip from Kolo Toure allowed Karim Matmour to score.
The Ivorians looked to have clinched progress to Thursday's semifinal when substitute Abdelkader Keita scored the tournament's best goal to date, a scorching 30 metre shot that gave the Algeria goalkeeper no chance.
With just seconds left, however, defender Madjid Bougherra was allowed to slip undetected in between the Ivorian defenders and head home a soft goal that forced the game into extra time.
Two minutes later Hameur Bouazza scored with his first touch in similar circumstances as the Ivorian defence was caught ball-watching.
Drogba forced a tremendous save from Fawzi Chaouchi before a controversial end to the match when Toure looked to have swept home for a 3-3 scoreline but was erroneously adjudged offside, as television replays afterwards proved.
Algeria now meet the winner of Monday's quarterfinal in Benguela between Cameroon and Egypt, the side they eliminated in a tempestuous World Cup play-off match last November.
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