The semi-final clash between the North African neighbours finished 1-1 after 90 minutes and extra time failed to separate the teams, who both had spells of territorial dominance on an artificial Khartoum Stadium pitch.
Tunisia scored from all five mandatory penalties, with Khaled Korbi converting the crucial final one after Algerian Hocine Metref failed to net his spot-kick and handed the initiative to their rivals.
Slama Gasdaoui put the Tunisians ahead on 18 minutes with his third goal of the biennial championship for home-based footballers, as he stabbed a low cross from the left past goalkeeper Mohamed Zemmamouche.
Algeria introduced 'super sub' Hadj Aissa nine minutes into the second half and persistent pressure paid dividends on 62 minutes when Abdelmoumene Djabou scored via a long-range shot.
Tired legs and minds meant extra time produced few chances to break the deadlock and both sides had clearly settled for a shootout long before the Mauritian referee blew for full time.
Sudanese supporters who packed the 42,000-capacity Al-Merreikh Stadium in Omdurman saw dreams of a first African title since the 1970 Cup of Nations triumph end as Mohamed Tahir and Mudathir Eltaib failed from the spot.
Angola converted all but one of their five kicks with 'Dani' scoring the penalty that took his team through despite winning just one of five matches in the tournament.
Favourites Sudan applied most of the first-half pressure and moved ahead in stoppage time when Saifeldin Ali Idris scored off a corner.
Although constantly on the back foot, the resilient Angolans levelled after 71 minutes when substitute Arsenio 'Love' Cabungula got the slightest of touches to an Osorio Carvalho free kick.