Algeria got the best out of their trip to Addis-Ababa, taking home the full points on offer in difficult conditions and on a very poor pitch.
The Ethiopians dominated the encounter in the first half with a very strong physical presence, and Salah Eddine Said went close to give the locals the lead in the 23rd and 27th minutes.
But it was against the run of play that the Fennec Foxes opened the score in the 35th minute by Soudani (assist by Yacine Brahimi) whose cross was deflected by an Ethiopian defender into his own net.
The match was more balanced in the second half, while Algeria's keeper Rais M'Bolhi had to still make a few important saves to keep his team ahead.
The Algerians were then able to extend their lead, finding the back of the net through Yacine Brahimi in the 84th minute following an excellent solo effort by Mahrez on the left wing.
Ethiopia managed to reduce the score line in referee’s optional time when Said netted from the penalty spot. But it was too little too late for the locals as new Algeria coach Christian Gourcuff got off to a great start.
Algeria are now due to host Mali on Wednesday while Malawi are at home to Ethiopia.