Captain Aissa Mandi scored an own goal and Napoli defender Faouzi Ghoulam gave away a penalty that was converted by Naim Sliti in a horror second half for Algeria as Tunisia rebounded from their defeat at the hands of Senegal on Sunday.
Sofiane Hanni pulled a goal back a minute into stoppage time for Algeria, but it came too late for them to mount a comeback.
Algeria, among the pre-tournament favourites, have one point and face Senegal next week, while Tunisia moved up to three points ahead of their final group game against Zimbabwe.
The result maintains a disappointing recent spell for Algeria, who fired coach Milovan Rajevac after they drew their opening World Cup group phase qualifier at home to Cameroon in October, and lost in the same competition to Nigeria in November.
Algeria started brightly on Thursday in a high-tempo opening spell with Yassine Brahimi having a free kick tipped over by Tunisia goalkeeper Aymen Mathlouthi and Leicester City forward Islam Slimani having a header cleared off the line -- all inside the opening 10 minutes.
Sunderland's Wahbi Khazri, restored to Tunisia's starting lineup, then had two half chances before Algeria's African Footballer of the Year Riyad Mahrez was set up by Slimani, but hit tamely at the goalkeeper in the 24th minute.
The opening goal arrived in the 50th minute when a cross from Youssef Msakni took a wicked deflection off the boot of Mandi and spun past Malik Asselah, who was making his debut in goal for Algeria in place of injured first choice Rais Mbolhi.
Sliti doubled the lead from the penalty spot 14 minutes later after Khazri had pounced on a weak back pass from Ghoulam and got away on goal, only for the defender to bring him down.
A Slimani effort was deflected narrowly wide as a largely ineffective Algeria produced a late rally, but the game had entered stoppage time when substitute Hanni hammered home unmarked.
Algeria had fought back from 2-1 down last Sunday to draw with Zimbabwe in their opener, but will have to move up a gear in their final group game if they are to stand any chance of progressing.
Senegal meet Zimbabwe later on Thursday in the other Group C match in Franceville.
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